Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of type complex or real of arbitrary kind parameter. More...

Detailed Description

Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of type complex or real of arbitrary kind parameter.

See the documentation of pm_fftnr for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of size getExpNext(size(data), 2) of the same type and kind as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftnr, only: getFFTF

type_of(data) :: fft(1 : getExpNext(size(data)))

fft(:) = getFFTF(data(:))

pm_fftnr::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftnr.F90:250

pm_fftnr
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftnr.F90:184

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTF.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftnr, only: getFFTF, getFFTI

6 use pm_distUnif, only: getUnifRand

7 use pm_mathCompare, only: isClose

8 use pm_err, only: setAsserted

9

10 implicit none

11

12 integer(IK) :: i

13 integer(IK) :: lenData

14 type(display_type) :: disp

15 disp = display_type(file = "main.out.F90")

16

17 do i = 1, 5

18 block

19 use pm_kind, only: TKG => CKS

20 real(TKG) :: reltol

21 complex(TKG), allocatable :: data(:), atad(:)

22 call disp%show("lenData = getUnifRand(5, 100)")

23 lenData = getUnifRand(5, 100)

24 call disp%show("lenData")

25 call disp%show( lenData )

26 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

27 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

28 call disp%show("data")

29 call disp%show( data )

30 call disp%skip()

31 call disp%show("atad = getFFTI(getFFTF(data))")

32 atad = getFFTI(getFFTF(data))

33 call disp%show("atad")

34 call disp%show( atad )

35 call disp%show("reltol = sqrt(epsilon(1._TKG))")

36 reltol = sqrt(epsilon(1._TKG))

37 call disp%show("reltol")

38 call disp%show( reltol )

39 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

40 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

41 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

42 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

43 call disp%skip()

44 end block

45

46 block

47 use pm_kind, only: TKG => CKD

48 real(TKG) :: reltol

49 complex(TKG), allocatable :: data(:), atad(:)

50 call disp%show("lenData = getUnifRand(5, 100)")

51 lenData = getUnifRand(5, 100)

52 call disp%show("lenData")

53 call disp%show( lenData )

54 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

55 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

56 call disp%show("data")

57 call disp%show( data )

58 call disp%skip()

59 call disp%show("atad = getFFTI(getFFTF(data))")

60 atad = getFFTI(getFFTF(data))

61 call disp%show("atad")

62 call disp%show( atad )

63 call disp%show("reltol = sqrt(epsilon(1._TKG))")

64 reltol = sqrt(epsilon(1._TKG))

65 call disp%show("reltol")

66 call disp%show( reltol )

67 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

68 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

69 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

70 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

71 call disp%skip()

72 end block

73

74 block

75 use pm_kind, only: TKG => CKH

76 real(TKG) :: reltol

77 complex(TKG), allocatable :: data(:), atad(:)

78 call disp%show("lenData = getUnifRand(5, 100)")

79 lenData = getUnifRand(5, 100)

80 call disp%show("lenData")

81 call disp%show( lenData )

82 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

83 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

84 call disp%show("data")

85 call disp%show( data )

86 call disp%skip()

87 call disp%show("atad = getFFTI(getFFTF(data))")

88 atad = getFFTI(getFFTF(data))

89 call disp%show("atad")

90 call disp%show( atad )

91 call disp%show("reltol = sqrt(epsilon(1._TKG))")

92 reltol = sqrt(epsilon(1._TKG))

93 call disp%show("reltol")

94 call disp%show( reltol )

95 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

96 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

97 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

98 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

99 call disp%skip()

100 end block

101

102 block

103 use pm_kind, only: TKG => RKS

104 real(TKG) :: reltol

105 real(TKG), allocatable :: data(:), atad(:)

106 call disp%show("lenData = getUnifRand(5, 100)")

107 lenData = getUnifRand(5, 100)

108 call disp%show("lenData")

109 call disp%show( lenData )

110 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

111 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

112 call disp%show("data")

113 call disp%show( data )

114 call disp%skip()

115 call disp%show("atad = getFFTI(getFFTF(data))")

116 atad = getFFTI(getFFTF(data))

117 call disp%show("atad")

118 call disp%show( atad )

119 call disp%show("reltol = sqrt(epsilon(1._TKG))")

120 reltol = sqrt(epsilon(1._TKG))

121 call disp%show("reltol")

122 call disp%show( reltol )

123 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

124 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

125 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

126 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

127 call disp%skip()

128 end block

129

130 block

131 use pm_kind, only: TKG => RKD

132 real(TKG) :: reltol

133 real(TKG), allocatable :: data(:), atad(:)

134 call disp%show("lenData = getUnifRand(5, 100)")

135 lenData = getUnifRand(5, 100)

136 call disp%show("lenData")

137 call disp%show( lenData )

138 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

139 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

140 call disp%show("data")

141 call disp%show( data )

142 call disp%skip()

143 call disp%show("atad = getFFTI(getFFTF(data))")

144 atad = getFFTI(getFFTF(data))

145 call disp%show("atad")

146 call disp%show( atad )

147 call disp%show("reltol = sqrt(epsilon(1._TKG))")

148 reltol = sqrt(epsilon(1._TKG))

149 call disp%show("reltol")

150 call disp%show( reltol )

151 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

152 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

153 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

154 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

155 call disp%skip()

156 end block

157

158 block

159 use pm_kind, only: TKG => RKH

160 real(TKG) :: reltol

161 real(TKG), allocatable :: data(:), atad(:)

162 call disp%show("lenData = getUnifRand(5, 100)")

163 lenData = getUnifRand(5, 100)

164 call disp%show("lenData")

165 call disp%show( lenData )

166 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

167 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

168 call disp%show("data")

169 call disp%show( data )

170 call disp%skip()

171 call disp%show("atad = getFFTI(getFFTF(data))")

172 atad = getFFTI(getFFTF(data))

173 call disp%show("atad")

174 call disp%show( atad )

175 call disp%show("reltol = sqrt(epsilon(1._TKG))")

176 reltol = sqrt(epsilon(1._TKG))

177 call disp%show("reltol")

178 call disp%show( reltol )

179 call disp%show("isClose(data, atad(1:size(data)), reltol = reltol)")

180 call disp%show( isClose(data, atad(1:size(data)), reltol = reltol) )

181 call disp%show("call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))")

182 call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

183 call disp%skip()

184 end block

185 end do

186

187end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftnr::getFFTI
Generate and return the Inverse (normalized by 2 / size(data)) Fourier Transform of a periodic sequen...
Definition: pm_fftnr.F90:428

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:535

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:843

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:571

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+29

4data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

5data

6(+1.31305480, +0.643765271), (+1.46137738, +0.780980766), (+1.21706915, +0.316828489E-2), (+1.98892832, +0.525719643), (+1.97828686, +0.122941554), (+1.47592556, +0.462218404), (+1.12475061, +0.941052079), (+1.69100726, +0.931249857), (+1.94960976, +0.667883515), (+1.61428106, +0.136653304), (+1.47523308, +0.743167043), (+1.17650926, +0.314282775E-1), (+1.65800571, +0.516092777E-2), (+1.90118670, +0.997002542), (+1.14983618, +0.840466797), (+1.60820365, +0.779335976), (+1.48306632, +0.248225987), (+1.85949612, +0.629457772), (+1.47554207, +0.715833127), (+1.65992403, +0.444152355E-1), (+1.12613869, +0.883065939), (+1.57965040, +0.475810587), (+1.93445504, +0.374805093), (+1.87351871, +0.878755152), (+1.31258082, +0.432980061E-2), (+1.24642062, +0.995212615), (+1.13268185, +0.852475822), (+1.34843040, +0.202596784), (+1.85042953, +0.721629143)

7

8atad = getFFTI(getFFTF(data))

9atad

10(+1.31305480, +0.643765211), (+1.46137738, +0.780980766), (+1.21706903, +0.316831470E-2), (+1.98892832, +0.525719643), (+1.97828686, +0.122941524), (+1.47592533, +0.462218463), (+1.12475061, +0.941051900), (+1.69100749, +0.931249797), (+1.94960988, +0.667883515), (+1.61428082, +0.136653334), (+1.47523296, +0.743167043), (+1.17650938, +0.314284191E-1), (+1.65800583, +0.516095757E-2), (+1.90118647, +0.997002542), (+1.14983582, +0.840466857), (+1.60820353, +0.779335976), (+1.48306632, +0.248225972), (+1.85949612, +0.629457772), (+1.47554195, +0.715833187), (+1.65992403, +0.444152504E-1), (+1.12613881, +0.883065820), (+1.57965028, +0.475810468), (+1.93445492, +0.374805272), (+1.87351882, +0.878755152), (+1.31258094, +0.432977080E-2), (+1.24642050, +0.995212674), (+1.13268173, +0.852475762), (+1.34843063, +0.202596784), (+1.85042965, +0.721629143), (+0.178813934E-6, +0.596046448E-7), (+0.178813934E-6, -0.298023224E-7), (+0.119209290E-6, +0.596046448E-7)

11reltol = sqrt(epsilon(1._TKG))

12reltol

13+0.345266977E-3

14isClose(data, atad(1:size(data)), reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+90

21data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

22data

23(+1.8425236698291867, +0.15460928815978225), (+1.3655682922864709, +0.31195587620975229), (+1.9046382032935421, +0.47370359459080358), (+1.7999565365978141, +0.46724004726204538), (+1.2719629809565394, +0.74253457747287033), (+1.2929562814321192, +0.96042699590761349), (+1.3674113077117429, +0.46295407021130985), (+1.8024481877215686, +0.59644662715962105), (+1.5178560155776188, +0.43644562821204069), (+1.4834118032652714, +0.75090626165644458), (+1.1837667867896906, +0.44524954745585876), (+1.6647385027166037, +0.55290660007866166), (+1.8673738366905646, +0.46933121064023575), (+1.2015905803721620, +0.95846650318666193), (+1.5666800327047699, +0.67948830413707462), (+1.6004363452534502, +0.22756811493249862), (+1.8601905631340387, +0.13686553191932227), (+1.2466011949211864, +0.67394935093888020), (+1.4315645266674160, +0.98181661046649238), (+1.1680802989039556, +0.76403714867951777), (+1.2056056712947982, +0.43916256035373658), (+1.9369911821659893, +0.56113523443305813), (+1.0382519658385920, +0.34300767554502720), (+1.0981403820947819, +0.23049494418490180), (+1.6896720213200336, +0.11835418238662931), (+1.7114706616452398, +0.93986923093457042), (+1.8490066115166384, +0.83753068551237542E-1), (+1.3011289123727052, +0.93059079551442370), (+1.1339198435143336, +0.37082242389669962), (+1.8646208176141190, +0.76050567997479646), (+1.7657674161244135, +0.94649715086118213), (+1.6326866027246527, +0.96927446771497572), (+1.5937416228236541, +0.96017218684626693), (+1.0918294221252931, +0.36424510500140561), (+1.3594262618285391, +0.60265892003578292), (+1.1502008029563238, +0.52775639586811396), (+1.9517633469290754, +0.41026152994781806), (+1.7965378451003973, +0.91624583055270803), (+1.8819000321975299, +0.47176963857047838E-1), (+1.4684216890104267, +0.20732103720486839E-1), (+1.6484204305820114, +0.55376248072537004), (+1.3735750986147912, +0.35574144132263641), (+1.9561954923527349, +0.53685159740125377), (+1.2154278857374692, +0.34099058361493051), (+1.7029315256296045, +0.60813476081649831), (+1.8961363212093820, +0.28539698944293790), (+1.6340032375141855, +0.70514486263358378), (+1.9879674680148223, +0.82204849969614702), (+1.4894812349467896, +0.50675551730861268), (+1.3832001405289542, +0.70655068496749662), (+1.3811834475606064, +0.31245207100395722), (+1.4460913470795440, +0.95629132932469962), (+1.3192427557383657, +0.58424495718800373), (+1.9067360902242652, +0.11094894799037691), (+1.8314874801594936, +0.65180832035670488), (+1.1836660202195992, +0.61152731288975071), (+1.2640323920871448, +0.47312892256775396), (+1.8658543284422273, +0.47099967786195596), (+1.8695213678566391, +0.56505860498294092E-1), (+1.7637626189811848, +0.49345431227504122), (+1.0854059677685972, +0.24108507423972048), (+1.1128901944895313, +0.58702105327662779), (+1.4660607685360354, +0.16810321876482215), (+1.9436886843439138, +0.17785497349068513), (+1.5542848396853175, +0.98471443841757378), (+1.3640247508239365, +0.45360555034248717), (+1.3519485469301435, +0.71164942594342262), (+1.7070820360484169, +0.25043978320806515), (+1.6753193227204726, +0.19736381392093183), (+1.0427792580900772, +0.19399295898135749), (+1.0434217515720343, +0.64848780436250131), (+1.6189441304750529, +0.84837397843875562), (+1.6632298645127874, +0.63592614410296666), (+1.7886636595976606, +0.34204785591428244), (+1.9188718345733966, +0.72337704326256724), (+1.9129285132324454, +0.29243172196287470), (+1.8722888324715874, +0.15966703469914212), (+1.2339919348551980, +0.69808266780026662), (+1.9551484545631599, +0.75855722844383100), (+1.5277325475367249, +0.38201764017888884E-2), (+1.8098135256384844, +0.44705800974091270E-1), (+1.7229408823380656, +0.29848872977613250), (+1.9690774298542415, +0.35116780917964618), (+1.2603100435538765, +0.85667856604058212), (+1.7652770087697811, +0.97537528487002978), (+1.3422666589525141, +0.73201485321733362), (+1.8728852615362841, +0.12246789269465608), (+1.8633328345119322, +0.42847903316619507), (+1.4721834744405449, +0.48648781241063921), (+1.8785872430887605, +0.47373367332300986)

24

25atad = getFFTI(getFFTF(data))

26atad

27(+1.8425236698291869, +0.15460928815978237), (+1.3655682922864714, +0.31195587620975262), (+1.9046382032935421, +0.47370359459080363), (+1.7999565365978141, +0.46724004726204599), (+1.2719629809565394, +0.74253457747287033), (+1.2929562814321189, +0.96042699590761393), (+1.3674113077117431, +0.46295407021130985), (+1.8024481877215688, +0.59644662715962138), (+1.5178560155776191, +0.43644562821204091), (+1.4834118032652717, +0.75090626165644503), (+1.1837667867896904, +0.44524954745585876), (+1.6647385027166035, +0.55290660007866244), (+1.8673738366905641, +0.46933121064023609), (+1.2015905803721620, +0.95846650318666227), (+1.5666800327047699, +0.67948830413707495), (+1.6004363452534502, +0.22756811493249915), (+1.8601905631340383, +0.13686553191932233), (+1.2466011949211864, +0.67394935093888053), (+1.4315645266674157, +0.98181661046649249), (+1.1680802989039551, +0.76403714867951744), (+1.2056056712947982, +0.43916256035373613), (+1.9369911821659889, +0.56113523443305824), (+1.0382519658385923, +0.34300767554502731), (+1.0981403820947819, +0.23049494418490191), (+1.6896720213200336, +0.11835418238662948), (+1.7114706616452400, +0.93986923093457064), (+1.8490066115166379, +0.83753068551237819E-1), (+1.3011289123727048, +0.93059079551442370), (+1.1339198435143336, +0.37082242389669945), (+1.8646208176141186, +0.76050567997479646), (+1.7657674161244135, +0.94649715086118191), (+1.6326866027246520, +0.96927446771497572), (+1.5937416228236541, +0.96017218684626671), (+1.0918294221252933, +0.36424510500140544), (+1.3594262618285391, +0.60265892003578270), (+1.1502008029563235, +0.52775639586811385), (+1.9517633469290754, +0.41026152994781784), (+1.7965378451003970, +0.91624583055270759), (+1.8819000321975303, +0.47176963857047560E-1), (+1.4684216890104267, +0.20732103720486644E-1), (+1.6484204305820114, +0.55376248072537004), (+1.3735750986147912, +0.35574144132263602), (+1.9561954923527347, +0.53685159740125354), (+1.2154278857374690, +0.34099058361493029), (+1.7029315256296047, +0.60813476081649809), (+1.8961363212093820, +0.28539698944293762), (+1.6340032375141860, +0.70514486263358300), (+1.9879674680148218, +0.82204849969614668), (+1.4894812349467896, +0.50675551730861257), (+1.3832001405289542, +0.70655068496749629), (+1.3811834475606064, +0.31245207100395705), (+1.4460913470795433, +0.95629132932469907), (+1.3192427557383659, +0.58424495718800362), (+1.9067360902242649, +0.11094894799037641), (+1.8314874801594936, +0.65180832035670444), (+1.1836660202195992, +0.61152731288975049), (+1.2640323920871444, +0.47312892256775374), (+1.8658543284422278, +0.47099967786195568), (+1.8695213678566387, +0.56505860498293897E-1), (+1.7637626189811844, +0.49345431227504111), (+1.0854059677685972, +0.24108507423972031), (+1.1128901944895313, +0.58702105327662735), (+1.4660607685360358, +0.16810321876482165), (+1.9436886843439134, +0.17785497349068474), (+1.5542848396853175, +0.98471443841757378), (+1.3640247508239367, +0.45360555034248706), (+1.3519485469301438, +0.71164942594342229), (+1.7070820360484165, +0.25043978320806509), (+1.6753193227204726, +0.19736381392093172), (+1.0427792580900770, +0.19399295898135721), (+1.0434217515720350, +0.64848780436250120), (+1.6189441304750531, +0.84837397843875562), (+1.6632298645127872, +0.63592614410296699), (+1.7886636595976608, +0.34204785591428255), (+1.9188718345733962, +0.72337704326256713), (+1.9129285132324447, +0.29243172196287459), (+1.8722888324715870, +0.15966703469914204), (+1.2339919348551980, +0.69808266780026640), (+1.9551484545631599, +0.75855722844383067), (+1.5277325475367249, +0.38201764017885276E-2), (+1.8098135256384840, +0.44705800974091339E-1), (+1.7229408823380656, +0.29848872977613239), (+1.9690774298542419, +0.35116780917964591), (+1.2603100435538761, +0.85667856604058179), (+1.7652770087697811, +0.97537528487002945), (+1.3422666589525138, +0.73201485321733295), (+1.8728852615362845, +0.12246789269465555), (+1.8633328345119322, +0.42847903316619473), (+1.4721834744405449, +0.48648781241063926), (+1.8785872430887605, +0.47373367332300970), (-0.33306690738754696E-15, -0.27755575615628914E-15), (-0.11102230246251565E-15, -0.61062266354383610E-15), (+0.33306690738754696E-15, -0.16653345369377348E-15), (+0.77715611723760958E-15, -0.22204460492503131E-15), (+0.77715611723760958E-15, -0.22204460492503131E-15), (+0.44408920985006262E-15, -0.55511151231257827E-15), (-0.33306690738754696E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, -0.11102230246251565E-15), (-0.22204460492503131E-15, -0.22204460492503131E-15), (-0.33306690738754696E-15, -0.11102230246251565E-15), (+0.0000000000000000, +0.30531133177191805E-15), (+0.0000000000000000, +0.11102230246251565E-15), (+0.44408920985006262E-15, +0.27755575615628914E-15), (+0.33306690738754696E-15, +0.19428902930940239E-15), (-0.44408920985006262E-15, +0.55511151231257827E-16), (+0.0000000000000000, -0.38857805861880479E-15), (-0.33306690738754696E-15, -0.16653345369377348E-15), (+0.0000000000000000, -0.30531133177191805E-15), (+0.0000000000000000, +0.11102230246251565E-15), (+0.66613381477509392E-15, +0.16653345369377348E-15), (+0.44408920985006262E-15, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.11102230246251565E-15), (+0.77715611723760958E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.16653345369377348E-15), (-0.11102230246251565E-15, +0.55511151231257827E-16), (+0.22204460492503131E-15, +0.33306690738754696E-15), (+0.55511151231257827E-15, +0.61062266354383610E-15), (+0.44408920985006262E-15, +0.49960036108132044E-15), (+0.22204460492503131E-15, +0.55511151231257827E-15), (+0.11102230246251565E-15, +0.13877787807814457E-15), (+0.99920072216264089E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.79797279894933126E-16), (+0.55511151231257827E-15, +0.47184478546569153E-15), (+0.44408920985006262E-15, +0.51347814888913490E-15), (+0.33306690738754696E-15, +0.72164496600635175E-15), (+0.77715611723760958E-15, +0.88817841970012523E-15), (+0.77715611723760958E-15, +0.10130785099704553E-14)

28reltol = sqrt(epsilon(1._TKG))

29reltol

30+0.14901161193847656E-7

31isClose(data, atad(1:size(data)), reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+33

38data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

39data

40(+1.74044241821365742940135266844919880, +0.545138489215447801128575124965403797), (+1.06538280904830760972982031136616608, +0.917860586824637895553707641811597222), (+1.15288308931903393647074526511699017, +0.150258681224842154861917826245306427), (+1.83384762168907295335333330111303809, +0.152495573410637395856618529308775872), (+1.96081173255418028662512943462986870, +0.624820802258758421756506126522485210), (+1.09239134102730913027268307957686505, +0.698821682455014549699752567790311699), (+1.00094504920253134839625548970003129, +0.478530390453708355959023874923240867), (+1.89686739078633759446892250995141615, +0.884820064701622299336665749516630029), (+1.38090573849567448278957963184089410, +0.398429846054928070550965621432903753), (+1.86195633754523994833625418468237141, +0.671018050079760120823829928776051279), (+1.59620691281389303975129760510362170, +0.514291678315336642600693595730136268), (+1.95185998038558762109735517446100959, +0.743846325983343456071051957303012694), (+1.68879269512091108382807998989934500, +0.332657900623057560261833864285310633), (+1.21584711685057880221622079923196069, +0.770348998266507225380445016288975443), (+1.35226776592891491209315216403273173, +0.624750016394350794740510472068748388), (+1.93859377212196713628682303077324588, +0.686308849080678927797974768121218111), (+1.75948533046422465580519744946655168, +0.937894106513788695124681224914338082), (+1.51175431386652916153452673523911017, +0.348114381836824943993838306953104225), (+1.04388047968736058976268887654169719, +0.595631920041360472125810197411429447), (+1.76548414274705887214975248917152724, +0.585639885118372291120350039296548441), (+1.49675402737132916490313171428750810, +0.562145439486489560144889684539690950), (+1.18830837992543005448800672017763295, +0.527079799885315012331779898736376913), (+1.73343691578638617453272340005581129, +0.418397315956498679279295620654118583), (+1.03890141270228605259978003155573384, +0.184379916762960840055714833185755820), (+1.61973097110333796726862553262280929, +0.929066919430759286784216299115104036), (+1.03317772351479148685508795368648527, +0.881457777266962194561511874003325943), (+1.92646909881113318285380349916580857, +0.514906680705881818721266049758924136), (+1.57785587519382756504728543891921465, +0.391220366332968770272565122309868501E-1), (+1.28132248873833554966634250437419733, +0.163259281791613720012575269424939128), (+1.31538700799965953574359298343423578, +0.745017759562153385723368266941052456), (+1.66047575494091835996008599330690698, +0.906175059138092115832720209921950639), (+1.30295123955589423429964753531765603, +0.149221112631989152086422292015951079), (+1.40693233294073888155876122571013136, +0.850349999995300094880714071711855578)

41

42atad = getFFTI(getFFTF(data))

43atad

44(+1.74044241821365742940135266844919899, +0.545138489215447801128575124965403797), (+1.06538280904830760972982031136616608, +0.917860586824637895553707641811597125), (+1.15288308931903393647074526511699017, +0.150258681224842154861917826245306427), (+1.83384762168907295335333330111303809, +0.152495573410637395856618529308775751), (+1.96081173255418028662512943462986928, +0.624820802258758421756506126522485114), (+1.09239134102730913027268307957686524, +0.698821682455014549699752567790311699), (+1.00094504920253134839625548970003167, +0.478530390453708355959023874923240770), (+1.89686739078633759446892250995141634, +0.884820064701622299336665749516629932), (+1.38090573849567448278957963184089390, +0.398429846054928070550965621432903849), (+1.86195633754523994833625418468237122, +0.671018050079760120823829928776051376), (+1.59620691281389303975129760510362151, +0.514291678315336642600693595730136171), (+1.95185998038558762109735517446100959, +0.743846325983343456071051957303012694), (+1.68879269512091108382807998989934500, +0.332657900623057560261833864285310729), (+1.21584711685057880221622079923196069, +0.770348998266507225380445016288975732), (+1.35226776592891491209315216403273211, +0.624750016394350794740510472068748292), (+1.93859377212196713628682303077324568, +0.686308849080678927797974768121218593), (+1.75948533046422465580519744946655149, +0.937894106513788695124681224914338082), (+1.51175431386652916153452673523911017, +0.348114381836824943993838306953104128), (+1.04388047968736058976268887654169739, +0.595631920041360472125810197411429351), (+1.76548414274705887214975248917152705, +0.585639885118372291120350039296548441), (+1.49675402737132916490313171428750810, +0.562145439486489560144889684539691142), (+1.18830837992543005448800672017763275, +0.527079799885315012331779898736376913), (+1.73343691578638617453272340005581148, +0.418397315956498679279295620654118583), (+1.03890141270228605259978003155573384, +0.184379916762960840055714833185755941), (+1.61973097110333796726862553262280891, +0.929066919430759286784216299115103651), (+1.03317772351479148685508795368648508, +0.881457777266962194561511874003325654), (+1.92646909881113318285380349916580857, +0.514906680705881818721266049758923751), (+1.57785587519382756504728543891921465, +0.391220366332968770272565122309867297E-1), (+1.28132248873833554966634250437419714, +0.163259281791613720012575269424939224), (+1.31538700799965953574359298343423559, +0.745017759562153385723368266941052745), (+1.66047575494091835996008599330690737, +0.906175059138092115832720209921950639), (+1.30295123955589423429964753531765603, +0.149221112631989152086422292015950934), (+1.40693233294073888155876122571013136, +0.850349999995300094880714071711855578), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (+0.192592994438723585305597794258492732E-33, -0.722223729145213444895991728469347744E-34), (+0.385185988877447170611195588516985464E-33, +0.722223729145213444895991728469347744E-34), (-0.481482486096808963263994485646231830E-33, +0.00000000000000000000000000000000000), (-0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-34), (-0.481482486096808963263994485646231830E-33, +0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (+0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.120370621524202240815998621411557957E-33), (+0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33), (-0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34), (+0.962964972193617926527988971292463659E-34, -0.337037740267766274284796139952362281E-33), (+0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (+0.962964972193617926527988971292463659E-34, -0.168518870133883137142398069976181140E-33), (+0.00000000000000000000000000000000000, +0.962964972193617926527988971292463659E-34), (+0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-34), (+0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33), (+0.192592994438723585305597794258492732E-33, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33), (+0.385185988877447170611195588516985464E-33, +0.168518870133883137142398069976181140E-33), (+0.962964972193617926527988971292463659E-34, -0.325000678115346050203196277811206485E-33), (+0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-33), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34), (+0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34)

45reltol = sqrt(epsilon(1._TKG))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, atad(1:size(data)), reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+35

55data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

56data

57+1.54913521, +1.93112087, +1.46059656, +1.65422523, +1.95582736, +1.81097126, +1.79266798, +1.96753597, +1.28625119, +1.99126053, +1.46677351, +1.51380563, +1.21963632, +1.06446409, +1.71874118, +1.72966552, +1.63986707, +1.02094483, +1.87844610, +1.74407244, +1.19959259, +1.26317191, +1.73306823, +1.41871691, +1.14971912, +1.58597219, +1.57264054, +1.80440080, +1.48208439, +1.82248938, +1.30333972, +1.49274182, +1.48876107, +1.96099305, +1.99778187

58

59atad = getFFTI(getFFTF(data))

60atad

61+1.54913521, +1.93112087, +1.46059656, +1.65422511, +1.95582700, +1.81097126, +1.79266787, +1.96753585, +1.28625119, +1.99126041, +1.46677351, +1.51380563, +1.21963620, +1.06446433, +1.71874094, +1.72966540, +1.63986707, +1.02094483, +1.87844610, +1.74407256, +1.19959259, +1.26317215, +1.73306823, +1.41871691, +1.14971900, +1.58597231, +1.57264042, +1.80440068, +1.48208427, +1.82248950, +1.30333972, +1.49274182, +1.48876095, +1.96099305, +1.99778175, +0.238418579E-6, +0.596046448E-7, +0.178813934E-6, +0.178813934E-6, +0.119209290E-6, -0.119209290E-6, +0.119209290E-6, -0.596046448E-7, +0.596046448E-7, +0.00000000, +0.596046448E-7, +0.238418579E-6, +0.119209290E-6, -0.119209290E-6, -0.596046448E-7, +0.00000000, +0.119209290E-6, -0.596046448E-7, -0.596046448E-7, +0.596046448E-7, +0.00000000, +0.00000000, +0.596046448E-7, -0.596046448E-7, +0.596046448E-7, +0.00000000, +0.178813934E-6, +0.00000000, +0.00000000

62reltol = sqrt(epsilon(1._TKG))

63reltol

64+0.345266977E-3

65isClose(data, atad(1:size(data)), reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+78

72data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

73data

74+1.7131519401058410, +1.5542717848353116, +1.6140978555644074, +1.1928918678069742, +1.3666301958339173, +1.6919823501040236, +1.6160079650739592, +1.4964782533219099, +1.8583693226802711, +1.5786576947096780, +1.3360231590314715, +1.5878763030731813, +1.5608353219429323, +1.3152639104757027, +1.7049675415819885, +1.5685015379903828, +1.6530469398918788, +1.8164030231253225, +1.0888532724781785, +1.5125006393147240, +1.1571317248831279, +1.4309542362041792, +1.2229628391384604, +1.1971816960487778, +1.4897989952237314, +1.9180661806159551, +1.5373927573228543, +1.0232033863200338, +1.5232955410352480, +1.3003892290439669, +1.5307487641777984, +1.4314178969758911, +1.9800622234353797, +1.4631613732353959, +1.8574980833592920, +1.5267239145802938, +1.7669138563117586, +1.1261392341860459, +1.8761506501306848, +1.8891556192293613, +1.2161835051133445, +1.3814508372684624, +1.9274563706138488, +1.0709663338796793, +1.6086130805809677, +1.9491814214044618, +1.5889133682292329, +1.2425703030584190, +1.9513117480825501, +1.6786316236966661, +1.5421629844251350, +1.5065283301562951, +1.3941724645198312, +1.6118936719962642, +1.8056906710422453, +1.2759112360488105, +1.5861714398096427, +1.5759835277420491, +1.9309870602057797, +1.7694711911547301, +1.3235328211203081, +1.0669509023779373, +1.7448250157270606, +1.4279275177495503, +1.5523257653323022, +1.9146372247315500, +1.2897569654274186, +1.0672163749822405, +1.9520925271529759, +1.6924658024306889, +1.0800911748159505, +1.3633255307701293, +1.4664701908212152, +1.7942981612851732, +1.2322647733154755, +1.8940401842442434, +1.4563465629007224, +1.3871197032370324

75

76atad = getFFTI(getFFTF(data))

77atad

78+1.7131519401058410, +1.5542717848353114, +1.6140978555644079, +1.1928918678069749, +1.3666301958339169, +1.6919823501040241, +1.6160079650739587, +1.4964782533219103, +1.8583693226802711, +1.5786576947096784, +1.3360231590314715, +1.5878763030731813, +1.5608353219429321, +1.3152639104757027, +1.7049675415819885, +1.5685015379903833, +1.6530469398918786, +1.8164030231253228, +1.0888532724781781, +1.5125006393147242, +1.1571317248831274, +1.4309542362041789, +1.2229628391384599, +1.1971816960487778, +1.4897989952237309, +1.9180661806159556, +1.5373927573228539, +1.0232033863200338, +1.5232955410352473, +1.3003892290439669, +1.5307487641777977, +1.4314178969758906, +1.9800622234353797, +1.4631613732353952, +1.8574980833592920, +1.5267239145802938, +1.7669138563117579, +1.1261392341860454, +1.8761506501306844, +1.8891556192293604, +1.2161835051133445, +1.3814508372684624, +1.9274563706138490, +1.0709663338796789, +1.6086130805809677, +1.9491814214044612, +1.5889133682292327, +1.2425703030584185, +1.9513117480825501, +1.6786316236966654, +1.5421629844251348, +1.5065283301562946, +1.3941724645198312, +1.6118936719962633, +1.8056906710422451, +1.2759112360488096, +1.5861714398096429, +1.5759835277420486, +1.9309870602057795, +1.7694711911547296, +1.3235328211203077, +1.0669509023779369, +1.7448250157270602, +1.4279275177495494, +1.5523257653323022, +1.9146372247315497, +1.2897569654274181, +1.0672163749822403, +1.9520925271529759, +1.6924658024306887, +1.0800911748159505, +1.3633255307701284, +1.4664701908212154, +1.7942981612851732, +1.2322647733154755, +1.8940401842442434, +1.4563465629007231, +1.3871197032370319, +0.55511151231257827E-15, -0.88817841970012523E-15, +0.44408920985006262E-15, -0.99920072216264089E-15, +0.55511151231257827E-15, -0.66613381477509392E-15, +0.88817841970012523E-15, -0.22204460492503131E-15, +0.99920072216264089E-15, -0.44408920985006262E-15, +0.77715611723760958E-15, -0.55511151231257827E-15, +0.77715611723760958E-15, -0.55511151231257827E-15, +0.55511151231257827E-15, +0.11102230246251565E-15, +0.66613381477509392E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.22204460492503131E-15, +0.11102230246251565E-15, +0.0000000000000000, +0.22204460492503131E-15, +0.44408920985006262E-15, +0.11102230246251565E-15, +0.33306690738754696E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.0000000000000000, +0.22204460492503131E-15, +0.33306690738754696E-15, +0.44408920985006262E-15, -0.33306690738754696E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.44408920985006262E-15, -0.33306690738754696E-15, +0.88817841970012523E-15, +0.0000000000000000, +0.99920072216264089E-15, +0.0000000000000000, +0.55511151231257827E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.66613381477509392E-15, +0.33306690738754696E-15, +0.99920072216264089E-15

79reltol = sqrt(epsilon(1._TKG))

80reltol

81+0.14901161193847656E-7

82isClose(data, atad(1:size(data)), reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+45

89data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

90data

91+1.90000309942204792118867219169394994, +1.81104992824667384282294471113911202, +1.41475792347536881242014128045703897, +1.42554736182899077156407026062685317, +1.05450898342109556753832087226871010, +1.13327218245146220638894294114470094, +1.00990074629284431601877811869295381, +1.92237336531221665596874922085657073, +1.96033723073248109200548514151355925, +1.53604180823366018322484915159624665, +1.19609773634672841398305749677298087, +1.00717956713768746340021212079437857, +1.18324181294420446651931944038825814, +1.80940012317894548057408288944518107, +1.52520555651432825751992391554773853, +1.65308599942306225743943921209844530, +1.00252243721793473127837933673314840, +1.27448676981097980966995605230704063, +1.61644514828303610720662249349497709, +1.17204803142830795267207437734672741, +1.22062910963147753664586476245574923, +1.26127011388440865813468924115154165, +1.94308462647669725915198154072596732, +1.06110630313709298895547909948801884, +1.73814131687842651892121940680543966, +1.31633739199487723091620034897597978, +1.56742930828798590135973182162716532, +1.86169788131413881080816270722054486, +1.22181002333082880513513209129022945, +1.79457134415715876006657367045109942, +1.86770857671897764203279661997913691, +1.39383168528246721017434588326701180, +1.59235146555917802819301538310925893, +1.83137102792806542728168151470296947, +1.72261259577788106183450645762974222, +1.50316375821286427720964470059139497, +1.52401574378407554150114441912717078, +1.32800035391556057775888777067641483, +1.48658701821924588853221597967611227, +1.03619416067167097262197273849402344, +1.51829970804351007833525164379419052, +1.53155943574815837801164214169551216, +1.17362183175692127763992062682744130, +1.01080381866919399789878824432390363, +1.56343407315657738627471216051623307

92

93atad = getFFTI(getFFTF(data))

94atad

95+1.90000309942204792118867219169395033, +1.81104992824667384282294471113911202, +1.41475792347536881242014128045703859, +1.42554736182899077156407026062685337, +1.05450898342109556753832087226871048, +1.13327218245146220638894294114470113, +1.00990074629284431601877811869295400, +1.92237336531221665596874922085657053, +1.96033723073248109200548514151355944, +1.53604180823366018322484915159624665, +1.19609773634672841398305749677298068, +1.00717956713768746340021212079437857, +1.18324181294420446651931944038825852, +1.80940012317894548057408288944518107, +1.52520555651432825751992391554773795, +1.65308599942306225743943921209844491, +1.00252243721793473127837933673314860, +1.27448676981097980966995605230704043, +1.61644514828303610720662249349497670, +1.17204803142830795267207437734672741, +1.22062910963147753664586476245574904, +1.26127011388440865813468924115154127, +1.94308462647669725915198154072596694, +1.06110630313709298895547909948801865, +1.73814131687842651892121940680543966, +1.31633739199487723091620034897597978, +1.56742930828798590135973182162716474, +1.86169788131413881080816270722054447, +1.22181002333082880513513209129022887, +1.79457134415715876006657367045109942, +1.86770857671897764203279661997913633, +1.39383168528246721017434588326701180, +1.59235146555917802819301538310925912, +1.83137102792806542728168151470296947, +1.72261259577788106183450645762974222, +1.50316375821286427720964470059139478, +1.52401574378407554150114441912717078, +1.32800035391556057775888777067641503, +1.48658701821924588853221597967611227, +1.03619416067167097262197273849402363, +1.51829970804351007833525164379419090, +1.53155943574815837801164214169551255, +1.17362183175692127763992062682744150, +1.01080381866919399789878824432390382, +1.56343407315657738627471216051623307, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.577778983316170755916793382775478196E-33, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.481482486096808963263994485646231830E-33, -0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33

96reltol = sqrt(epsilon(1._TKG))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, atad(1:size(data)), reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+82

106data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

107data

108(+1.31404901, +0.309514344), (+1.77235937, +0.231363535), (+1.92657971, +0.705951750), (+1.51297438, +0.685293436), (+1.39053214, +0.383710265), (+1.40557718, +0.231540442), (+1.50482559, +0.583831310), (+1.08532119, +0.457510471), (+1.27815115, +0.678705812), (+1.25544953, +0.795623660), (+1.88932145, +0.841232300), (+1.95060825, +0.477213264), (+1.05919075, +0.455328763), (+1.79189289, +0.214868069), (+1.98985410, +0.921761572), (+1.05767894, +0.920303106), (+1.09638858, +0.840152383), (+1.79860020, +0.143861651), (+1.81811571, +0.517433107), (+1.84259105, +0.495444775), (+1.70052302, +0.421280324), (+1.28423023, +0.324038267E-1), (+1.22432446, +0.885587513), (+1.03914833, +0.218294621), (+1.34942079, +0.311417580), (+1.50081491, +0.661574423), (+1.66407633, +0.916631937), (+1.60032141, +0.346443832), (+1.25451612, +0.374899983), (+1.96557832, +0.844831407), (+1.38116276, +0.935523808), (+1.47278214, +0.154969096E-1), (+1.18506765, +0.258206666), (+1.11749804, +0.823948979E-1), (+1.43580616, +0.625400901), (+1.21616793, +0.786060214), (+1.57610762, +0.484167755), (+1.78572297, +0.770005882), (+1.67521620, +0.466605783), (+1.03425264, +0.735152841), (+1.90578818, +0.297138512), (+1.79817009, +0.181651115E-1), (+1.56640005, +0.649279296), (+1.09729958, +0.842905760), (+1.42578721, +0.147175312), (+1.00268781, +0.775241494), (+1.88249087, +0.273643553), (+1.48456633, +0.339395583), (+1.23358941, +0.845139444), (+1.09340143, +0.345663846), (+1.82130599, +0.839589596), (+1.32871866, +0.328339458), (+1.97021818, +0.134408355), (+1.79807067, +0.466732562), (+1.41365218, +0.984163165), (+1.11047184, +0.808011889E-1), (+1.82063401, +0.837347150), (+1.29573226, +0.322984159), (+1.26650715, +0.276439667), (+1.94392908, +0.752056181), (+1.93235159, +0.409801245), (+1.71575320, +0.350548506), (+1.82460952, +0.447915733), (+1.07654500, +0.741452813), (+1.76156962, +0.516710579), (+1.32874978, +0.867710888), (+1.05040979, +0.222734511), (+1.20189726, +0.139370024), (+1.72244823, +0.789711058), (+1.46775937, +0.297588229), (+1.24416876, +0.417826533), (+1.32311797, +0.938270211), (+1.06083417, +0.857812822), (+1.96843100, +0.721479952), (+1.11965835, +0.959687829E-1), (+1.76250672, +0.775602281), (+1.90422893, +0.561307669E-1), (+1.23987770, +0.421479523), (+1.75531960, +0.777453542), (+1.17892027, +0.662424326), (+1.84200966, +0.138455749), (+1.18324971, +0.318155527)

109

110atad = getFFTI(getFFTF(data))

111atad

112(+1.31404912, +0.309514314), (+1.77235925, +0.231363744), (+1.92657936, +0.705951691), (+1.51297402, +0.685293436), (+1.39053202, +0.383710265), (+1.40557718, +0.231540412), (+1.50482535, +0.583831251), (+1.08532107, +0.457510263), (+1.27815127, +0.678705692), (+1.25544977, +0.795623720), (+1.88932133, +0.841232359), (+1.95060825, +0.477213442), (+1.05919075, +0.455328822), (+1.79189324, +0.214868248), (+1.98985398, +0.921761632), (+1.05767906, +0.920302987), (+1.09638846, +0.840152383), (+1.79860032, +0.143861800), (+1.81811547, +0.517433167), (+1.84259093, +0.495444685), (+1.70052278, +0.421280205), (+1.28423047, +0.324038714E-1), (+1.22432423, +0.885587573), (+1.03914809, +0.218294650), (+1.34942102, +0.311417639), (+1.50081503, +0.661574602), (+1.66407609, +0.916631997), (+1.60032153, +0.346444070), (+1.25451612, +0.374899983), (+1.96557844, +0.844831645), (+1.38116264, +0.935523808), (+1.47278214, +0.154968966E-1), (+1.18506777, +0.258206606), (+1.11749816, +0.823948905E-1), (+1.43580616, +0.625400782), (+1.21616817, +0.786060095), (+1.57610750, +0.484167546), (+1.78572297, +0.770005822), (+1.67521608, +0.466605723), (+1.03425276, +0.735152602), (+1.90578818, +0.297138512), (+1.79817033, +0.181651711E-1), (+1.56639993, +0.649279177), (+1.09729958, +0.842905760), (+1.42578721, +0.147175193), (+1.00268793, +0.775241375), (+1.88249087, +0.273643434), (+1.48456645, +0.339395553), (+1.23358941, +0.845139384), (+1.09340143, +0.345663726), (+1.82130575, +0.839589357), (+1.32871866, +0.328339338), (+1.97021794, +0.134408087), (+1.79807055, +0.466732532), (+1.41365218, +0.984162927), (+1.11047173, +0.808011144E-1), (+1.82063365, +0.837347150), (+1.29573226, +0.322984219), (+1.26650715, +0.276439667), (+1.94392872, +0.752055883), (+1.93235135, +0.409801185), (+1.71575308, +0.350548714), (+1.82460952, +0.447915614), (+1.07654488, +0.741452575), (+1.76156986, +0.516710639), (+1.32874954, +0.867710829), (+1.05040991, +0.222734451), (+1.20189714, +0.139369875), (+1.72244835, +0.789710999), (+1.46775937, +0.297588199), (+1.24416900, +0.417826474), (+1.32311809, +0.938270092), (+1.06083417, +0.857812881), (+1.96843076, +0.721480310), (+1.11965847, +0.959689021E-1), (+1.76250648, +0.775602043), (+1.90422893, +0.561309010E-1), (+1.23987770, +0.421479642), (+1.75531971, +0.777453542), (+1.17892039, +0.662424445), (+1.84200966, +0.138455749), (+1.18324959, +0.318155497), (+0.417232513E-6, -0.298023224E-7), (+0.238418579E-6, +0.298023224E-7), (+0.238418579E-6, +0.745058060E-7), (+0.596046448E-7, -0.149011612E-7), (+0.476837158E-6, +0.268220901E-6), (+0.178813934E-6, +0.208616257E-6), (+0.298023224E-6, -0.104308128E-6), (-0.119209290E-6, -0.178813934E-6), (+0.119209290E-6, +0.00000000), (+0.596046448E-7, -0.223517418E-6), (-0.596046448E-7, -0.745058060E-7), (-0.119209290E-6, -0.119209290E-6), (+0.119209290E-6, -0.596046448E-7), (+0.00000000, -0.167638063E-7), (+0.119209290E-6, +0.134110451E-6), (-0.596046448E-7, +0.670552254E-7), (+0.119209290E-6, +0.238418579E-6), (+0.00000000, +0.268220901E-6), (+0.596046448E-7, +0.268220901E-6), (-0.596046448E-7, +0.208616257E-6), (+0.119209290E-6, +0.372529030E-6), (+0.00000000, +0.268220901E-6), (+0.238418579E-6, +0.00000000), (+0.00000000, +0.596046448E-7), (+0.119209290E-6, +0.178813934E-6), (+0.596046448E-7, -0.298023224E-7), (+0.596046448E-7, +0.596046448E-7), (+0.238418579E-6, -0.894069672E-7), (+0.00000000, +0.00000000), (-0.596046448E-7, +0.298023224E-7), (+0.596046448E-7, +0.894069672E-7), (+0.178813934E-6, +0.104308128E-6), (+0.238418579E-6, +0.327825546E-6), (+0.596046448E-7, +0.178813934E-6), (+0.596046448E-7, +0.156462193E-6), (+0.119209290E-6, +0.149011612E-6), (+0.238418579E-6, +0.327825546E-6), (-0.596046448E-7, +0.316649675E-6), (+0.417232513E-6, -0.298023224E-7), (+0.238418579E-6, -0.149011612E-7), (+0.178813934E-6, +0.163912773E-6), (+0.178813934E-6, +0.298023224E-7), (+0.178813934E-6, -0.298023224E-7), (+0.417232513E-6, -0.298023224E-7), (+0.596046448E-7, +0.178813934E-6), (-0.119209290E-6, +0.894069672E-7)

113reltol = sqrt(epsilon(1._TKG))

114reltol

115+0.345266977E-3

116isClose(data, atad(1:size(data)), reltol = reltol)

117T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

118call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+82

123data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

124data

125(+1.4380632534577655, +0.43503584041237775E-1), (+1.3726338012314008, +0.10421749474472419), (+1.8563148432392880, +0.61876223755555659), (+1.2897912940158625, +0.99077667036581829E-1), (+1.7739895591087487, +0.49494363712251388), (+1.3074166580429019, +0.87779881360927570), (+1.1660181102539093, +0.26599836919382236), (+1.0162674001149319, +0.99323593993338122E-1), (+1.9267288637983737, +0.70450300352916329E-1), (+1.2040487942217375, +0.37263685751851261), (+1.7532014998811494, +0.49584064078561008), (+1.3771441813539020, +0.34984448068353280), (+1.1713814553587787, +0.13412837232226860E-1), (+1.7768286542640885, +0.64007540360648196), (+1.0282059129961796, +0.38534163827478640), (+1.4744941097180544, +0.55018394305946794E-2), (+1.3053488289234032, +0.68835939967432436), (+1.5660927233845050, +0.56683784099735435), (+1.5792494485447048, +0.92686943854307868E-1), (+1.9765570694194745, +0.97214622591122535), (+1.0270385300928864, +0.87266951018254901), (+1.5610755328019112, +0.26142274022999723), (+1.5152317713249719, +0.27205511900298007), (+1.5167011927342786, +0.67686288448271470), (+1.5763169813255118, +0.20046180576567951), (+1.9703351785704406, +0.89001081129484683E-1), (+1.4869353699386849, +0.69298028495254771), (+1.3084137757050871, +0.53807060390811490), (+1.4512325389997329, +0.34579515900087043), (+1.4198987583465263, +0.52815115429653603), (+1.7790042181030117, +0.51503987675407426E-1), (+1.8005438912633474, +0.24554685089250361), (+1.6959667744322984, +0.72298350690579005), (+1.9359370907886158, +0.36730658831484064), (+1.8351416160463412, +0.93353892431892815), (+1.5487887873728015, +0.10254055289348829), (+1.2548532719138863, +0.20455220265086027), (+1.2648326746674941, +0.69190662414285875), (+1.3058874546056249, +0.35798111570456481), (+1.4525142030427540, +0.58582366892689630), (+1.7642094411158884, +0.36447703027484690), (+1.3965799169438982, +0.75780606316978771), (+1.1629797130830357, +0.74834996650420504), (+1.3721576205355535, +0.80520375336261230), (+1.2441747019255938, +0.71020158260236765), (+1.5402772236841868, +0.39056970942773994), (+1.3776692518294655, +0.89936638971441996), (+1.4172287746360408, +0.94744238979973372), (+1.8756525308908358, +0.13550671952382154), (+1.7249777364523149, +0.78283157066466957), (+1.7038758927267823, +0.33023015980659454), (+1.7575255182569487, +0.79179348519336545), (+1.0697551157138023, +0.72478639875373796), (+1.4032706788182399, +0.63701954377762271), (+1.1314459470033338, +0.41289444161758271), (+1.7215681513874639, +0.10078557304974955), (+1.5097950368421356, +0.31538073624080898E-1), (+1.4593904669629145, +0.37769292753077433), (+1.0575466511136544, +0.10130340458025988), (+1.8205237357846924, +0.90130229184950150), (+1.1278207256634345, +0.51319761077488923), (+1.1251867259926309, +0.97006286995115765), (+1.3506434232013529, +0.14150973134196576), (+1.2457085761941795, +0.11450465493620066), (+1.2087470825887978, +0.23978595282481052), (+1.3700781717260362, +0.43161355119435596), (+1.5760646296927934, +0.29574255700267604), (+1.3740771670317029, +0.99416467689785148), (+1.6045107942975396, +0.47869889754327288), (+1.2828629438001062, +0.92883537455950571), (+1.8261207780228428, +0.54770099477819212), (+1.4822368216883270, +0.66425706867399126E-1), (+1.7177582126291933, +0.28028467272492119), (+1.6828310275764811, +0.72639383023547222), (+1.6698851253958291, +0.93699756802904854), (+1.2620708203875286, +0.82634757868306319E-1), (+1.3121957945092682, +0.21549470235145707), (+1.1085291267638944, +0.81868521205957934), (+1.7558701893470299, +0.64421429485312487), (+1.6614698310204763, +0.57568765610233985), (+1.6701007503884102, +0.69083652080787006), (+1.5243730907509849, +0.65075635496417650)

126

127atad = getFFTI(getFFTF(data))

128atad

129(+1.4380632534577655, +0.43503584041237775E-1), (+1.3726338012314014, +0.10421749474472439), (+1.8563148432392877, +0.61876223755555659), (+1.2897912940158629, +0.99077667036582440E-1), (+1.7739895591087484, +0.49494363712251394), (+1.3074166580429016, +0.87779881360927570), (+1.1660181102539089, +0.26599836919382241), (+1.0162674001149317, +0.99323593993338538E-1), (+1.9267288637983739, +0.70450300352916606E-1), (+1.2040487942217382, +0.37263685751851294), (+1.7532014998811492, +0.49584064078561041), (+1.3771441813539025, +0.34984448068353335), (+1.1713814553587787, +0.13412837232226971E-1), (+1.7768286542640885, +0.64007540360648230), (+1.0282059129961796, +0.38534163827478646), (+1.4744941097180546, +0.55018394305952900E-2), (+1.3053488289234032, +0.68835939967432447), (+1.5660927233845050, +0.56683784099735468), (+1.5792494485447048, +0.92686943854308049E-1), (+1.9765570694194743, +0.97214622591122590), (+1.0270385300928866, +0.87266951018254879), (+1.5610755328019112, +0.26142274022999701), (+1.5152317713249714, +0.27205511900298007), (+1.5167011927342786, +0.67686288448271470), (+1.5763169813255118, +0.20046180576567954), (+1.9703351785704406, +0.89001081129485016E-1), (+1.4869353699386845, +0.69298028495254771), (+1.3084137757050871, +0.53807060390811490), (+1.4512325389997327, +0.34579515900087060), (+1.4198987583465263, +0.52815115429653570), (+1.7790042181030115, +0.51503987675407523E-1), (+1.8005438912633474, +0.24554685089250355), (+1.6959667744322984, +0.72298350690578972), (+1.9359370907886162, +0.36730658831484037), (+1.8351416160463412, +0.93353892431892782), (+1.5487887873728017, +0.10254055289348786), (+1.2548532719138863, +0.20455220265086022), (+1.2648326746674941, +0.69190662414285820), (+1.3058874546056252, +0.35798111570456453), (+1.4525142030427540, +0.58582366892689575), (+1.7642094411158884, +0.36447703027484679), (+1.3965799169438982, +0.75780606316978738), (+1.1629797130830359, +0.74834996650420493), (+1.3721576205355532, +0.80520375336261218), (+1.2441747019255938, +0.71020158260236754), (+1.5402772236841868, +0.39056970942773961), (+1.3776692518294658, +0.89936638971441973), (+1.4172287746360406, +0.94744238979973328), (+1.8756525308908361, +0.13550671952382126), (+1.7249777364523151, +0.78283157066466957), (+1.7038758927267823, +0.33023015980659437), (+1.7575255182569487, +0.79179348519336501), (+1.0697551157138028, +0.72478639875373763), (+1.4032706788182399, +0.63701954377762227), (+1.1314459470033338, +0.41289444161758215), (+1.7215681513874639, +0.10078557304974917), (+1.5097950368421356, +0.31538073624080599E-1), (+1.4593904669629145, +0.37769292753077421), (+1.0575466511136544, +0.10130340458025999), (+1.8205237357846924, +0.90130229184950106), (+1.1278207256634347, +0.51319761077488879), (+1.1251867259926307, +0.97006286995115698), (+1.3506434232013529, +0.14150973134196537), (+1.2457085761941800, +0.11450465493620027), (+1.2087470825887978, +0.23978595282481041), (+1.3700781717260362, +0.43161355119435618), (+1.5760646296927929, +0.29574255700267604), (+1.3740771670317029, +0.99416467689785137), (+1.6045107942975396, +0.47869889754327283), (+1.2828629438001060, +0.92883537455950538), (+1.8261207780228426, +0.54770099477819190), (+1.4822368216883273, +0.66425706867398904E-1), (+1.7177582126291933, +0.28028467272492108), (+1.6828310275764806, +0.72639383023547233), (+1.6698851253958287, +0.93699756802904877), (+1.2620708203875286, +0.82634757868306014E-1), (+1.3121957945092684, +0.21549470235145679), (+1.1085291267638941, +0.81868521205957923), (+1.7558701893470297, +0.64421429485312420), (+1.6614698310204763, +0.57568765610233941), (+1.6701007503884102, +0.69083652080786973), (+1.5243730907509847, +0.65075635496417661), (+0.0000000000000000, -0.26367796834847468E-15), (+0.11102230246251565E-15, -0.72164496600635175E-15), (+0.55511151231257827E-15, +0.0000000000000000), (+0.11102230246251565E-15, -0.11102230246251565E-15), (+0.11102230246251565E-15, -0.83266726846886741E-16), (+0.44408920985006262E-15, -0.38857805861880479E-15), (-0.11102230246251565E-15, -0.41633363423443370E-15), (+0.11102230246251565E-15, -0.22204460492503131E-15), (+0.0000000000000000, -0.27755575615628914E-15), (+0.33306690738754696E-15, -0.27755575615628914E-15), (+0.44408920985006262E-15, +0.55511151231257827E-16), (+0.33306690738754696E-15, -0.11102230246251565E-15), (+0.22204460492503131E-15, -0.13530843112619095E-15), (+0.44408920985006262E-15, -0.38857805861880479E-15), (-0.22204460492503131E-15, +0.16653345369377348E-15), (+0.11102230246251565E-15, +0.16653345369377348E-15), (-0.55511151231257827E-15, +0.16653345369377348E-15), (+0.44408920985006262E-15, -0.13877787807814457E-16), (-0.22204460492503131E-15, +0.26367796834847468E-15), (+0.0000000000000000, +0.22204460492503131E-15), (+0.0000000000000000, +0.44408920985006262E-15), (+0.0000000000000000, +0.0000000000000000), (+0.22204460492503131E-15, +0.83266726846886741E-16), (+0.11102230246251565E-15, +0.0000000000000000), (-0.22204460492503131E-15, -0.11102230246251565E-15), (+0.11102230246251565E-15, -0.55511151231257827E-16), (+0.0000000000000000, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.33306690738754696E-15), (-0.11102230246251565E-15, +0.16653345369377348E-15), (+0.0000000000000000, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.22204460492503131E-15), (+0.0000000000000000, +0.27755575615628914E-15), (+0.22204460492503131E-15, +0.49960036108132044E-15), (+0.0000000000000000, +0.33306690738754696E-15), (+0.22204460492503131E-15, +0.27755575615628914E-15), (+0.11102230246251565E-15, +0.66613381477509392E-15), (+0.44408920985006262E-15, +0.83266726846886741E-15), (+0.22204460492503131E-15, +0.25673907444456745E-15), (+0.66613381477509392E-15, +0.36082248300317588E-15), (+0.0000000000000000, +0.16653345369377348E-15), (+0.33306690738754696E-15, +0.61062266354383610E-15), (+0.0000000000000000, +0.49960036108132044E-15), (+0.22204460492503131E-15, +0.55511151231257827E-15), (+0.11102230246251565E-15, +0.73552275381416621E-15), (+0.55511151231257827E-15, +0.95062846483529029E-15)

130reltol = sqrt(epsilon(1._TKG))

131reltol

132+0.14901161193847656E-7

133isClose(data, atad(1:size(data)), reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+28

140data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

141data

142(+1.82423188198782901723808050438203887, +0.795329997631070518220283679912845006), (+1.20765299097075322088748766750286460, +0.286077905161638796755753385988595316), (+1.85209983991520835259504114824963211, +0.940485794639484393934410360029335636), (+1.03226177697782463474573519097325920, +0.530211521965870072226618586911178978E-1), (+1.70321931992488538834171390946780730, +0.793269933624151243830491506815015420), (+1.51189324850094822270913221619943088, +0.815252705980896984943114669457583373), (+1.30203212019825290302998097102164556, +0.308013489583398178458571717614979321), (+1.40529466131090360377300647705669483, +0.589461363664195126775514040110149350), (+1.03462440397438387331886843078634214, +0.153531074215471084651837988111149854), (+1.40201910289085400623241412035244627, +0.922213974688134321950182229159139579), (+1.08293736691582688881531754749455806, +0.538893758214451993753335982845160981), (+1.39621992893551059447088582159146120, +0.254469614056116197214435177788555525), (+1.16371115812879050371393777616897698, +0.619520278722757305049057980763496131), (+1.86349980388444046053832231785069771, +0.322952490772845044544842847029013540), (+1.57785799713876602970447135945402911, +0.460404347918612347225343790691947703), (+1.84075711819050472901406734968512126, +0.182587942643793857738451553221496574), (+1.90076739933234301408864275484617029, +0.219133655558488210566522217367704673), (+1.04140762072971828832091743511586258, +0.363998589668025998397750658735717641), (+1.69383585352670074452381167385632208, +0.901607789125042677954221426589513063), (+1.36988316988646667517200386692841801, +0.359879659458661577158364708733928220), (+1.45446516220201055865966522414474366, +0.695045004443372354995539464690712957), (+1.78406665482101643516609878784106151, +0.131200961746649458187413804792555742), (+1.49551478320142199490210900630596589, +0.300471901909921182062370560683208584E-1), (+1.81142637701411008506974317107021464, +0.463257946849385590616236014860772246), (+1.39673127263254020359400736801717034, +0.610849211819670545757711932103220929), (+1.11304337640242880087589019426474118, +0.950816489476030161902098852962963806), (+1.40858314733179159554682750986271031, +0.731420737239711043169347072386861576), (+1.51373142378594845208068363097774005, +0.250044383976034919546066153806652860)

143

144atad = getFFTI(getFFTF(data))

145atad

146(+1.82423188198782901723808050438203867, +0.795329997631070518220283679912845006), (+1.20765299097075322088748766750286460, +0.286077905161638796755753385988595509), (+1.85209983991520835259504114824963211, +0.940485794639484393934410360029335636), (+1.03226177697782463474573519097325958, +0.530211521965870072226618586911177533E-1), (+1.70321931992488538834171390946780710, +0.793269933624151243830491506815015324), (+1.51189324850094822270913221619943088, +0.815252705980896984943114669457583084), (+1.30203212019825290302998097102164556, +0.308013489583398178458571717614979225), (+1.40529466131090360377300647705669522, +0.589461363664195126775514040110149158), (+1.03462440397438387331886843078634214, +0.153531074215471084651837988111149758), (+1.40201910289085400623241412035244646, +0.922213974688134321950182229159139676), (+1.08293736691582688881531754749455787, +0.538893758214451993753335982845160885), (+1.39621992893551059447088582159146159, +0.254469614056116197214435177788555428), (+1.16371115812879050371393777616897640, +0.619520278722757305049057980763496131), (+1.86349980388444046053832231785069771, +0.322952490772845044544842847029013492), (+1.57785799713876602970447135945402872, +0.460404347918612347225343790691947799), (+1.84075711819050472901406734968512107, +0.182587942643793857738451553221496502), (+1.90076739933234301408864275484617010, +0.219133655558488210566522217367704866), (+1.04140762072971828832091743511586258, +0.363998589668025998397750658735717641), (+1.69383585352670074452381167385632189, +0.901607789125042677954221426589513063), (+1.36988316988646667517200386692841820, +0.359879659458661577158364708733928268), (+1.45446516220201055865966522414474347, +0.695045004443372354995539464690712957), (+1.78406665482101643516609878784106151, +0.131200961746649458187413804792555983), (+1.49551478320142199490210900630596589, +0.300471901909921182062370560683208103E-1), (+1.81142637701411008506974317107021522, +0.463257946849385590616236014860772391), (+1.39673127263254020359400736801717015, +0.610849211819670545757711932103220929), (+1.11304337640242880087589019426474137, +0.950816489476030161902098852962963710), (+1.40858314733179159554682750986270993, +0.731420737239711043169347072386861673), (+1.51373142378594845208068363097774044, +0.250044383976034919546066153806653053), (-0.288889491658085377958396691387739098E-33, -0.481482486096808963263994485646231830E-34), (+0.288889491658085377958396691387739098E-33, +0.481482486096808963263994485646231830E-34), (-0.288889491658085377958396691387739098E-33, -0.240741243048404481631997242823115915E-33), (+0.192592994438723585305597794258492732E-33, -0.240741243048404481631997242823115915E-34)

147reltol = sqrt(epsilon(1._TKG))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, atad(1:size(data)), reltol = reltol)

151T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+70

157data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

158data

159+1.48300505, +1.59075010, +1.86679637, +1.47306192, +1.64788091, +1.54975414, +1.99167919, +1.67331028, +1.30311501, +1.20834267, +1.55529904, +1.83953309, +1.64190841, +1.37811351, +1.55709481, +1.84238052, +1.39228368, +1.99394965, +1.47348547, +1.49150872, +1.51960886, +1.17103982, +1.15118611, +1.83953536, +1.40827072, +1.31568646, +1.89784181, +1.99205124, +1.14858711, +1.76654649, +1.20794141, +1.57888341, +1.54258132, +1.72680068, +1.26864266, +1.00812101, +1.07711136, +1.25916338, +1.88158751, +1.24784410, +1.79778957, +1.26395059, +1.63439465, +1.54662347, +1.82328796, +1.25950086, +1.87690675, +1.43758368, +1.73822141, +1.94326472, +1.99510741, +1.13248599, +1.22954249, +1.23641777, +1.37385893, +1.79784060, +1.43642902, +1.26709199, +1.70226324, +1.73203754, +1.66467011, +1.58190775, +1.64557910, +1.79626155, +1.26554894, +1.16268575, +1.23576260, +1.16489100, +1.34692931, +1.22395754

160

161atad = getFFTI(getFFTF(data))

162atad

163+1.48300505, +1.59074998, +1.86679602, +1.47306168, +1.64788055, +1.54975390, +1.99167883, +1.67330968, +1.30311489, +1.20834267, +1.55529916, +1.83953309, +1.64190841, +1.37811327, +1.55709493, +1.84238029, +1.39228344, +1.99394941, +1.47348523, +1.49150848, +1.51960862, +1.17103982, +1.15118599, +1.83953512, +1.40827036, +1.31568670, +1.89784157, +1.99205136, +1.14858699, +1.76654649, +1.20794129, +1.57888365, +1.54258132, +1.72680068, +1.26864266, +1.00812101, +1.07711124, +1.25916326, +1.88158727, +1.24784374, +1.79778934, +1.26395059, +1.63439465, +1.54662347, +1.82328796, +1.25950062, +1.87690663, +1.43758345, +1.73822093, +1.94326448, +1.99510694, +1.13248587, +1.22954226, +1.23641753, +1.37385881, +1.79784024, +1.43642867, +1.26709175, +1.70226288, +1.73203743, +1.66466987, +1.58190775, +1.64557910, +1.79626155, +1.26554871, +1.16268563, +1.23576283, +1.16489089, +1.34692955, +1.22395730, +0.119209290E-6, +0.357627869E-6, -0.178813934E-6, +0.00000000, -0.119209290E-6, -0.596046448E-7, +0.238418579E-6, +0.238418579E-6, -0.119209290E-6, +0.238418579E-6, +0.178813934E-6, -0.596046448E-7, +0.178813934E-6, +0.119209290E-6, +0.238418579E-6, -0.596046448E-7, +0.596046448E-7, +0.119209290E-6, +0.238418579E-6, -0.298023224E-6, +0.238418579E-6, -0.417232513E-6, +0.238418579E-6, -0.596046448E-7, +0.596046448E-7, -0.596046448E-7, -0.178813934E-6, -0.178813934E-6, -0.596046448E-7, +0.00000000, -0.596046448E-7, +0.119209290E-6, -0.596046448E-7, +0.238418579E-6, +0.596046448E-7, -0.596046448E-7, +0.00000000, -0.119209290E-6, +0.00000000, +0.119209290E-6, -0.596046448E-7, +0.238418579E-6, +0.238418579E-6, +0.00000000, +0.298023224E-6, +0.178813934E-6, +0.596046448E-7, +0.178813934E-6, +0.00000000, +0.357627869E-6, +0.357627869E-6, +0.596046448E-7, +0.417232513E-6, +0.00000000, +0.119209290E-6, -0.596046448E-7, -0.119209290E-6, +0.596046448E-7

164reltol = sqrt(epsilon(1._TKG))

165reltol

166+0.345266977E-3

167isClose(data, atad(1:size(data)), reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+58

174data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

175data

176+1.0276526324041182, +1.8678842059044016, +1.1439035730171880, +1.3289404976721040, +1.9408131855797202, +1.7460120968896908, +1.3231620940646165, +1.7554205572713513, +1.7036476884407898, +1.7831464339453240, +1.6163764172757165, +1.1840330213886729, +1.6025152685396824, +1.5787825261071753, +1.4211677959397893, +1.9377724916618850, +1.9049641867446425, +1.4326893503365856, +1.3218668421387629, +1.4557035788638100, +1.6713609007069383, +1.9366095665506071, +1.9664539113561177, +1.1057189034371537, +1.7072890688249673, +1.9330701303804496, +1.5337147327992597, +1.3193120709542085, +1.1159673167641937, +1.1762207616441231, +1.4356369861826237, +1.0446670399567148, +1.3789087925494143, +1.1270782630484777, +1.7889642434224307, +1.9300716465860985, +1.0899437726433248, +1.0235792061257385, +1.3750078500690641, +1.6704749306011148, +1.4642389125357977, +1.1611853397378999, +1.7172650318019251, +1.9097956599110582, +1.1595119209602414, +1.7821894947771986, +1.3165922215750956, +1.1743819549584549, +1.9761229261157403, +1.3863245653433327, +1.0012577666424143, +1.4735560603389677, +1.2856106171524224, +1.5976492806255673, +1.9736360353580451, +1.5870236026767834, +1.6254186643740745, +1.1749305861037271

177

178atad = getFFTI(getFFTF(data))

179atad

180+1.0276526324041182, +1.8678842059044016, +1.1439035730171878, +1.3289404976721042, +1.9408131855797204, +1.7460120968896906, +1.3231620940646163, +1.7554205572713510, +1.7036476884407901, +1.7831464339453242, +1.6163764172757160, +1.1840330213886729, +1.6025152685396824, +1.5787825261071748, +1.4211677959397888, +1.9377724916618848, +1.9049641867446423, +1.4326893503365856, +1.3218668421387629, +1.4557035788638100, +1.6713609007069383, +1.9366095665506069, +1.9664539113561172, +1.1057189034371540, +1.7072890688249678, +1.9330701303804494, +1.5337147327992589, +1.3193120709542083, +1.1159673167641937, +1.1762207616441225, +1.4356369861826233, +1.0446670399567146, +1.3789087925494146, +1.1270782630484777, +1.7889642434224302, +1.9300716465860983, +1.0899437726433252, +1.0235792061257383, +1.3750078500690639, +1.6704749306011142, +1.4642389125357982, +1.1611853397378999, +1.7172650318019249, +1.9097956599110577, +1.1595119209602420, +1.7821894947771979, +1.3165922215750956, +1.1743819549584549, +1.9761229261157400, +1.3863245653433329, +1.0012577666424145, +1.4735560603389675, +1.2856106171524231, +1.5976492806255671, +1.9736360353580449, +1.5870236026767830, +1.6254186643740747, +1.1749305861037271, +0.99920072216264089E-15, +0.77715611723760958E-15, +0.66613381477509392E-15, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.66613381477509392E-15

181reltol = sqrt(epsilon(1._TKG))

182reltol

183+0.14901161193847656E-7

184isClose(data, atad(1:size(data)), reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+23

191data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

192data

193+1.13314497006325396522532681673624682, +1.83831755915881779593198080486264951, +1.05214561321790100067406111157749835, +1.77997071464707550681996448230855410, +1.32771110164272049044496488042021494, +1.31611647229787981448051997183574554, +1.29169894773317629785403016123183993, +1.62465557438521422291238379370850598, +1.84398341194244135772710197702382106, +1.80433892224564174038592729917300494, +1.57754001138815448508773044853911516, +1.00050147905045863944996254951585055, +1.08060005046565156292372752167403396, +1.48592186198501299802402560421507860, +1.77806425641518122907331610494288779, +1.08114258512235586182319843500244590, +1.05989366480059902256757177324074649, +1.98161492596153568405946346659286189, +1.61001508811813151593386290677131364, +1.50413748462919217078012797914941485, +1.73615200584579620568398943345667357, +1.41917347957789116694043328528201997, +1.76050392430150272005336662598773430

194

195atad = getFFTI(getFFTF(data))

196atad

197+1.13314497006325396522532681673624682, +1.83831755915881779593198080486264970, +1.05214561321790100067406111157749835, +1.77997071464707550681996448230855449, +1.32771110164272049044496488042021494, +1.31611647229787981448051997183574534, +1.29169894773317629785403016123183955, +1.62465557438521422291238379370850636, +1.84398341194244135772710197702382145, +1.80433892224564174038592729917300494, +1.57754001138815448508773044853911536, +1.00050147905045863944996254951585055, +1.08060005046565156292372752167403434, +1.48592186198501299802402560421507880, +1.77806425641518122907331610494288798, +1.08114258512235586182319843500244609, +1.05989366480059902256757177324074649, +1.98161492596153568405946346659286189, +1.61001508811813151593386290677131345, +1.50413748462919217078012797914941523, +1.73615200584579620568398943345667357, +1.41917347957789116694043328528202016, +1.76050392430150272005336662598773391, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000, -0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, -0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33

198reltol = sqrt(epsilon(1._TKG))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, atad(1:size(data)), reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+80

208data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

209data

210(+1.05017304, +0.781148911), (+1.62112093, +0.516624451E-1), (+1.77203381, +0.711943984), (+1.83107662, +0.973234177), (+1.52558434, +0.202420115), (+1.41454172, +0.373347700), (+1.63023925, +0.383106053), (+1.31399059, +0.188997328), (+1.08734131, +0.138738155), (+1.36829305, +0.300741732), (+1.21585596, +0.643058956), (+1.48060095, +0.599654496), (+1.64602172, +0.779452085), (+1.06709790, +0.379715979), (+1.15965319, +0.986012220), (+1.59586155, +0.153939426), (+1.62293983, +0.927480936), (+1.38253248, +0.413838327), (+1.80243456, +0.966794193), (+1.01935339, +0.452774167), (+1.97882473, +0.137481213), (+1.87147129, +0.415641844), (+1.32485580, +0.452117622), (+1.97917724, +0.698174000), (+1.48439729, +0.526732266), (+1.71140099, +0.636847019), (+1.87958312, +0.499688268), (+1.41941440, +0.186428308), (+1.31701434, +0.422100425E-1), (+1.44014323, +0.653082907), (+1.69153142, +0.245471001E-1), (+1.29534173, +0.133156776), (+1.81803787, +0.217317939E-1), (+1.29564738, +0.813898504), (+1.91891885, +0.112167776), (+1.22060752, +0.262327850), (+1.48032904, +0.992502749), (+1.33142591, +0.241549492), (+1.94749939, +0.569918096), (+1.67476249, +0.638668656), (+1.38309205, +0.935280561), (+1.39112759, +0.644654870), (+1.26004505, +0.370366812), (+1.12055850, +0.789506614), (+1.65623689, +0.252310157), (+1.72207761, +0.253182054), (+1.21863234, +0.472257316), (+1.83422732, +0.648355603), (+1.35582852, +0.890235424), (+1.33531499, +0.193581581), (+1.74480128, +0.336829603), (+1.36214507, +0.632282197), (+1.72452807, +0.133373380), (+1.31365585, +0.956253827), (+1.16230440, +0.775389135), (+1.48735714, +0.718743026), (+1.58974004, +0.503692627E-1), (+1.97619641, +0.589509428), (+1.54857707, +0.194839001), (+1.46630025, +0.593055010), (+1.70915318, +0.916497350), (+1.18605494, +0.445340157), (+1.46970105, +0.461596251E-2), (+1.98139441, +0.665533602), (+1.53984785, +0.318173409), (+1.29387331, +0.753509402E-1), (+1.39726090, +0.161776543E-1), (+1.36477280, +0.586325705), (+1.04392242, +0.600433111), (+1.03773665, +0.817673922), (+1.80059528, +0.713889480), (+1.49066710, +0.276407123), (+1.02793002, +0.177666485), (+1.58454442, +0.945249081), (+1.19649839, +0.643863559), (+1.52273870, +0.232729375), (+1.75378788, +0.145565152), (+1.59814310, +0.513481140), (+1.97125316, +0.308390677), (+1.80777276, +0.432370603)

211

212atad = getFFTI(getFFTF(data))

213atad

214(+1.05017304, +0.781148911), (+1.62112093, +0.516625121E-1), (+1.77203357, +0.711943984), (+1.83107626, +0.973234177), (+1.52558422, +0.202420026), (+1.41454148, +0.373347670), (+1.63023901, +0.383105814), (+1.31399012, +0.188997388), (+1.08734155, +0.138738066), (+1.36829305, +0.300741643), (+1.21585596, +0.643058896), (+1.48060071, +0.599654615), (+1.64602172, +0.779452205), (+1.06709790, +0.379716009), (+1.15965319, +0.986012101), (+1.59586132, +0.153939337), (+1.62293983, +0.927480936), (+1.38253212, +0.413838387), (+1.80243444, +0.966794074), (+1.01935315, +0.452774286), (+1.97882462, +0.137481242), (+1.87147105, +0.415641785), (+1.32485545, +0.452117801), (+1.97917688, +0.698173881), (+1.48439741, +0.526732326), (+1.71140099, +0.636847019), (+1.87958288, +0.499688566), (+1.41941428, +0.186428577), (+1.31701446, +0.422101542E-1), (+1.44014323, +0.653082967), (+1.69153130, +0.245471913E-1), (+1.29534173, +0.133156866), (+1.81803787, +0.217316598E-1), (+1.29564738, +0.813898385), (+1.91891873, +0.112167671), (+1.22060752, +0.262327790), (+1.48032904, +0.992502511), (+1.33142591, +0.241549373), (+1.94749939, +0.569917798), (+1.67476225, +0.638668180), (+1.38309193, +0.935280442), (+1.39112771, +0.644654989), (+1.26004505, +0.370366603), (+1.12055850, +0.789506555), (+1.65623689, +0.252310157), (+1.72207761, +0.253182024), (+1.21863246, +0.472257286), (+1.83422720, +0.648355424), (+1.35582852, +0.890235305), (+1.33531475, +0.193581492), (+1.74480128, +0.336829484), (+1.36214471, +0.632282019), (+1.72452807, +0.133373231), (+1.31365585, +0.956253529), (+1.16230440, +0.775388956), (+1.48735690, +0.718742728), (+1.58974004, +0.503692031E-1), (+1.97619629, +0.589509487), (+1.54857695, +0.194839016), (+1.46629989, +0.593054831), (+1.70915306, +0.916497111), (+1.18605494, +0.445340037), (+1.46970105, +0.461587077E-2), (+1.98139405, +0.665533423), (+1.53984785, +0.318173409), (+1.29387331, +0.753509030E-1), (+1.39726102, +0.161776245E-1), (+1.36477268, +0.586325526), (+1.04392242, +0.600433230), (+1.03773665, +0.817673683), (+1.80059552, +0.713889301), (+1.49066687, +0.276406944), (+1.02792978, +0.177666634), (+1.58454418, +0.945249081), (+1.19649827, +0.643863559), (+1.52273858, +0.232729301), (+1.75378788, +0.145565182), (+1.59814310, +0.513481259), (+1.97125340, +0.308390766), (+1.80777276, +0.432370573), (-0.596046448E-7, +0.00000000), (+0.596046448E-7, -0.253319740E-6), (+0.417232513E-6, +0.596046448E-7), (+0.298023224E-6, -0.596046448E-7), (+0.298023224E-6, +0.201165676E-6), (+0.357627869E-6, -0.149011612E-7), (+0.357627869E-6, +0.104308128E-6), (+0.357627869E-6, +0.149011612E-6), (-0.596046448E-7, -0.894069672E-7), (+0.00000000, -0.178813934E-6), (+0.00000000, -0.596046448E-7), (+0.298023224E-6, -0.193715096E-6), (+0.00000000, -0.111758709E-6), (+0.00000000, -0.268220901E-6), (+0.119209290E-6, -0.130385160E-7), (+0.596046448E-7, -0.126659870E-6), (-0.119209290E-6, +0.192783773E-6), (+0.178813934E-6, +0.596046448E-7), (+0.119209290E-6, +0.253319740E-6), (+0.178813934E-6, +0.253319740E-6), (-0.596046448E-7, +0.298023224E-6), (+0.119209290E-6, +0.208616257E-6), (+0.119209290E-6, +0.357627869E-6), (+0.00000000, +0.387430191E-6), (-0.596046448E-7, +0.00000000), (+0.119209290E-6, -0.298023224E-7), (+0.00000000, +0.149011612E-6), (+0.178813934E-6, +0.298023224E-7), (+0.00000000, +0.00000000), (+0.00000000, +0.149011612E-6), (-0.596046448E-7, +0.298023224E-7), (-0.119209290E-6, +0.298023224E-6), (+0.596046448E-7, +0.894069672E-7), (+0.596046448E-7, +0.208616257E-6), (+0.178813934E-6, +0.298023224E-6), (+0.178813934E-6, +0.298023224E-6), (+0.178813934E-6, +0.275671482E-6), (+0.00000000, +0.268220901E-6), (+0.00000000, +0.238418579E-6), (+0.00000000, +0.447034836E-6), (+0.178813934E-6, +0.596046448E-7), (+0.238418579E-6, -0.894069672E-7), (+0.119209290E-6, +0.223517418E-6), (+0.119209290E-6, +0.119209290E-6), (+0.119209290E-6, +0.298023224E-7), (+0.596046448E-7, -0.149011612E-7), (+0.00000000, +0.721774995E-7), (-0.178813934E-6, +0.894069672E-7)

215reltol = sqrt(epsilon(1._TKG))

216reltol

217+0.345266977E-3

218isClose(data, atad(1:size(data)), reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+26

225data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

226data

227(+1.3083752807791524, +0.64014448202753815E-2), (+1.7565029869932327, +0.31571608460154499E-1), (+1.7822702144417317, +0.11286663161753296), (+1.4832133105676788, +0.79223497334702631), (+1.0879008314890375, +0.36865702621683349), (+1.3874364544332676, +0.35222678169906019), (+1.9378092642734623, +0.65729538849686253), (+1.4183560786676455, +0.73179568713946830), (+1.1256996402170376, +0.90908863637645332), (+1.9393035787901374, +0.14881267401873088), (+1.4084065738009377, +0.61856455721884274), (+1.6788646576159303, +0.40955127942713410), (+1.8219620086768156, +0.73638942693644638), (+1.4270128282990755, +0.29484527687719309), (+1.3042367036981513, +0.51150241467745483), (+1.9638518378999605, +0.91726611573415096), (+1.1538392111164897, +0.14614699057315783), (+1.7510603731027623, +0.95732989972558691), (+1.8900257981808080, +0.78094625389793282E-1), (+1.2959816890139453, +0.80305640067189177), (+1.9223808805497384, +0.21008285101138213), (+1.5317081062682816, +0.74350867706643664), (+1.3752540011111565, +0.34518389287462314E-1), (+1.2292863807492660, +0.86474268194362047), (+1.2346959403861304, +0.59014774070529596), (+1.3376380731659983, +0.44147959686531213)

228

229atad = getFFTI(getFFTF(data))

230atad

231(+1.3083752807791522, +0.64014448202752983E-2), (+1.7565029869932323, +0.31571608460154832E-1), (+1.7822702144417319, +0.11286663161753299), (+1.4832133105676781, +0.79223497334702631), (+1.0879008314890373, +0.36865702621683338), (+1.3874364544332676, +0.35222678169906046), (+1.9378092642734623, +0.65729538849686242), (+1.4183560786676450, +0.73179568713946841), (+1.1256996402170374, +0.90908863637645332), (+1.9393035787901369, +0.14881267401873091), (+1.4084065738009377, +0.61856455721884274), (+1.6788646576159296, +0.40955127942713410), (+1.8219620086768149, +0.73638942693644616), (+1.4270128282990751, +0.29484527687719309), (+1.3042367036981515, +0.51150241467745461), (+1.9638518378999597, +0.91726611573415062), (+1.1538392111164897, +0.14614699057315769), (+1.7510603731027619, +0.95732989972558669), (+1.8900257981808082, +0.78094625389793254E-1), (+1.2959816890139451, +0.80305640067189155), (+1.9223808805497382, +0.21008285101138213), (+1.5317081062682818, +0.74350867706643631), (+1.3752540011111569, +0.34518389287462259E-1), (+1.2292863807492660, +0.86474268194362036), (+1.2346959403861304, +0.59014774070529585), (+1.3376380731659983, +0.44147959686531191), (+0.44408920985006262E-15, -0.55511151231257827E-16), (+0.22204460492503131E-15, +0.0000000000000000), (+0.0000000000000000, +0.16653345369377348E-15), (+0.77715611723760958E-15, +0.41633363423443370E-15), (+0.66613381477509392E-15, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.72164496600635175E-15)

232reltol = sqrt(epsilon(1._TKG))

233reltol

234+0.14901161193847656E-7

235isClose(data, atad(1:size(data)), reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+83

242data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

243data

244(+1.13187720737950028100770694825962730, +0.407427626316981433641791381104488880), (+1.78166204059749244100968327880295318, +0.185418375652885836861665784919921573), (+1.41108146583415915469574200797556489, +0.260999397620868577150061507438895372), (+1.04364202747934624966710058617286883, +0.214283461013738142320189448564568768), (+1.38906095711021373502351878500888736, +0.148965035131943413520430157113559644), (+1.72526063648021988690685847634041604, +0.130433035960354764872825348529054503), (+1.13820477698394743366593772753788918, +0.970055661525400104415001755519579658), (+1.00823021114744288086651600956653582, +0.777566266653855014289747811719375820), (+1.09687398838638393756750712905410602, +0.283320410056815394618914777199246262), (+1.89013743892539715835883007139724521, +0.587737388023187749528765093761835936), (+1.83295613840680708588524236371636519, +0.343373790497964906969648765097717939), (+1.33088078745910196857539731639067069, +0.673687193400526666970917754024582454), (+1.71636449295606310407413557899754643, +0.965326458973500793773289981533399044), (+1.67669280388609374430228264340617996, +0.112174869527862516072681939741478158), (+1.22104686626444707620117107219211999, +0.800436415835308034620023888425598856E-1), (+1.42479297374216274286374538200044208, +0.688544623023134072268561380660418764), (+1.70453642357414263769549515428880079, +0.716604549534597695077135259788078731), (+1.34197843032814458692849815042811492, +0.587141817523683445079216018397219330), (+1.82466958794482375408441861528457874, +0.938445408417153061298303658637152825), (+1.42421830999478334436387576416913927, +0.983480342610685748394819001446776773), (+1.87144058228799087477486148709542189, +0.830080145846223263503359991411186788), (+1.73688694088982157280291020219897932, +0.250497328842921943722921852595794389), (+1.30319877153898750899398275943619327, +0.227330054060093372769199094638018950), (+1.21907630920191100460441936119416283, +0.490273024853667764839425175275824973), (+1.89049372094643713949786961781559368, +0.374929000021352783603460030402991402), (+1.51335528136343769198242371805403012, +0.562273828431652607518854249920026329E-1), (+1.51410919632429273176789231290137224, +0.263650286125148628305421096428866995), (+1.18871969226175913903639159771594344, +0.378009302317600337955313373598738751), (+1.55589451760465514119418112786954668, +0.276526995851854028858897801032552378), (+1.10141830641791091698747866652623143, +0.642199318378967452756955804278033404), (+1.12920753928196679774517488159777644, +0.892766526712175304279897430208022002), (+1.98090102837704702047218323905889572, +0.684453892500346803259354808817870930), (+1.16495579759874840547929172833007790, +0.904989542700808010289996993805999727), (+1.77445403239736831371961325636103532, +0.383504282700230115479126317564823110), (+1.75625621434971018811621364178281009, +0.478610777959946703654758700364645122), (+1.11271625909960622024386351260176168, +0.469510719497317687954495949145756175), (+1.69943944894325055060857315420909235, +0.603351980319438356867763562975516095), (+1.99110740659912411785523296687678577, +0.866276346720836574789705808986977627), (+1.82932062957335136751345964271021274, +0.526135321843628896974576037018889512), (+1.86745440536430916256031063873865462, +0.377962330661330888331443709550324291), (+1.59771953180793496282127830849350537, +0.593054524722137900941325151680091934), (+1.25482257204358458230337948410007911, +0.523525426954881899718575704667332878), (+1.44837330278500490301166022876044965, +0.677954254623828449339560072603175038E-3), (+1.91675914383536491311445694565429753, +0.720053154567285610612946474972543989E-1), (+1.20601896270967311884046011785510920, +0.825979787058427679251365492557801081), (+1.44050570875436196445085941201831045, +0.118021213744674028697640268207840056), (+1.34797797581795582899022498455809370, +0.993724268608192369673187753602937417), (+1.76154761902953673016743619998202242, 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+0.993864348158840093348000172530273565E-1), (+1.64516227030516109587130765270126041, +0.302244470679637629332502370142767430), (+1.78099353621626905390047636883557405, +0.589956334609225660487654106113900709), (+1.76946848427452329622555279134513932, +0.877840729236953311258442211706569036), (+1.12379255507712243443899729309199516, +0.159794693953863169475143135445405732), (+1.37828065967259258297354769665143836, +0.759095011643608071345691647150950003), (+1.13723877373499960104386533571512670, +0.288357630010526060850310099134534464), (+1.03180235557731214060800413889888195, +0.217060555209429875035558656544871170), (+1.04202776854710134183434201944276962, +0.333262163159203476302463512305836284), (+1.54816353189988916986985672990458190, +0.432989855035696953403649265482411099), (+1.04031533768449454188478364351731631, +0.556066191973470324360623010108767198E-1), (+1.37482437453644649778896120662577558, +0.851908934661043159411963706408269670), (+1.73571868184694004491772301039532751, +0.248776634307204332974890748936669213), (+1.40848534387790480681663491142434750, +0.622606890931200768737287260377812438), (+1.62001900713545176117493556039549984, +0.402555005847046485177800854853509354), (+1.98505645730554562939553439383849094, +0.978724574117466080537796755956245378E-1), (+1.81972331466107771556754110826331280, +0.188756054205108963020502207269712470), (+1.10116677860099113394560201836627721, +0.649139251344842742600279049391965132), (+1.51307466607643237368062389542212157, +0.422850593396754260562118519511460338), (+1.79058360224815910513607548334229570, +0.768567399612780914648240310518223990), (+1.69462275669362693897180444541754032, +0.527592990329312827552843568001493024), (+1.18972167742343058789009307568751203, +0.391392152587134898162395154411542676), (+1.59131309526422021585609622137022531, +0.977398135172619108363280493292790674), (+1.47025667228567035007170217519468050, +0.483343394558054447961362896139402212)

245

246atad = getFFTI(getFFTF(data))

247atad

248(+1.13187720737950028100770694825962730, +0.407427626316981433641791381104488976), (+1.78166204059749244100968327880295356, +0.185418375652885836861665784919921333), (+1.41108146583415915469574200797556508, +0.260999397620868577150061507438895324), (+1.04364202747934624966710058617286902, +0.214283461013738142320189448564568624), (+1.38906095711021373502351878500888736, +0.148965035131943413520430157113559644), (+1.72526063648021988690685847634041604, +0.130433035960354764872825348529054021), (+1.13820477698394743366593772753788899, +0.970055661525400104415001755519579755), (+1.00823021114744288086651600956653582, +0.777566266653855014289747811719375531), (+1.09687398838638393756750712905410602, +0.283320410056815394618914777199246166), (+1.89013743892539715835883007139724578, +0.587737388023187749528765093761835743), (+1.83295613840680708588524236371636557, +0.343373790497964906969648765097718036), (+1.33088078745910196857539731639067069, +0.673687193400526666970917754024582647), 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+0.993864348158840093348000172530274889E-1), (+1.64516227030516109587130765270126079, +0.302244470679637629332502370142767622), (+1.78099353621626905390047636883557482, +0.589956334609225660487654106113901190), (+1.76946848427452329622555279134513970, +0.877840729236953311258442211706569132), (+1.12379255507712243443899729309199516, +0.159794693953863169475143135445405973), (+1.37828065967259258297354769665143836, +0.759095011643608071345691647150949907), (+1.13723877373499960104386533571512690, +0.288357630010526060850310099134534513), (+1.03180235557731214060800413889888195, +0.217060555209429875035558656544871315), (+1.04202776854710134183434201944276962, +0.333262163159203476302463512305836525), (+1.54816353189988916986985672990458229, +0.432989855035696953403649265482411003), (+1.04031533768449454188478364351731670, +0.556066191973470324360623010108767078E-1), (+1.37482437453644649778896120662577558, +0.851908934661043159411963706408269670), (+1.73571868184694004491772301039532732, +0.248776634307204332974890748936669213), (+1.40848534387790480681663491142434750, +0.622606890931200768737287260377812534), (+1.62001900713545176117493556039550003, +0.402555005847046485177800854853509787), (+1.98505645730554562939553439383849133, +0.978724574117466080537796755956248508E-1), (+1.81972331466107771556754110826331299, +0.188756054205108963020502207269712446), (+1.10116677860099113394560201836627721, +0.649139251344842742600279049391965132), (+1.51307466607643237368062389542212176, +0.422850593396754260562118519511461012), (+1.79058360224815910513607548334229608, +0.768567399612780914648240310518223893), (+1.69462275669362693897180444541754013, +0.527592990329312827552843568001493216), (+1.18972167742343058789009307568751184, +0.391392152587134898162395154411542773), (+1.59131309526422021585609622137022550, +0.977398135172619108363280493292791060), (+1.47025667228567035007170217519468031, +0.483343394558054447961362896139402164), (-0.674075480535532548569592279904724561E-33, +0.962964972193617926527988971292463659E-34), (+0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.385185988877447170611195588516985464E-33, +0.481482486096808963263994485646231830E-33), (-0.962964972193617926527988971292463659E-34, +0.132407683676622464897598483552713753E-33), (-0.385185988877447170611195588516985464E-33, +0.409260113182287618774395312799297055E-33), (-0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33), (-0.577778983316170755916793382775478196E-33, +0.237731977510299425611597277287826966E-33), (+0.00000000000000000000000000000000000, -0.264815367353244929795196967105427506E-33), (-0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000), (+0.00000000000000000000000000000000000, -0.168518870133883137142398069976181140E-33), (-0.770371977754894341222391177033970927E-33, +0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33), (-0.674075480535532548569592279904724561E-33, -0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.144444745829042688979198345693869549E-33), (-0.385185988877447170611195588516985464E-33, +0.216667118743564033468797518540804323E-33), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.481482486096808963263994485646231830E-33, -0.481482486096808963263994485646231830E-34), (+0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000), (-0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34), (+0.00000000000000000000000000000000000, -0.481482486096808963263994485646231830E-34), (-0.577778983316170755916793382775478196E-33, -0.481482486096808963263994485646231830E-34), (-0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33), (-0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33), (-0.192592994438723585305597794258492732E-33, -0.337037740267766274284796139952362281E-33), (-0.385185988877447170611195588516985464E-33, -0.120370621524202240815998621411557957E-33), (+0.962964972193617926527988971292463659E-34, +0.00000000000000000000000000000000000), (-0.770371977754894341222391177033970927E-33, -0.240741243048404481631997242823115915E-34), (+0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-33), (-0.577778983316170755916793382775478196E-33, -0.337037740267766274284796139952362281E-33), (-0.288889491658085377958396691387739098E-33, +0.722223729145213444895991728469347744E-34), (-0.481482486096808963263994485646231830E-33, -0.288889491658085377958396691387739098E-33), (-0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33), (-0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33), (-0.962964972193617926527988971292463659E-34, +0.144444745829042688979198345693869549E-33), (-0.962964972193617926527988971292463659E-33, -0.240741243048404481631997242823115915E-34), (+0.00000000000000000000000000000000000, +0.108333559371782016734398759270402162E-33), (-0.481482486096808963263994485646231830E-33, -0.240741243048404481631997242823115915E-33), (-0.192592994438723585305597794258492732E-33, -0.337037740267766274284796139952362281E-33), (-0.577778983316170755916793382775478196E-33, -0.288889491658085377958396691387739098E-33), (+0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33), (-0.385185988877447170611195588516985464E-33, -0.349074802420186498366396002093518076E-33), (-0.192592994438723585305597794258492732E-33, -0.216667118743564033468797518540804323E-33), (-0.770371977754894341222391177033970927E-33, -0.674075480535532548569592279904724561E-33), (-0.385185988877447170611195588516985464E-33, -0.337037740267766274284796139952362281E-33), (-0.481482486096808963263994485646231830E-33, -0.469445423944388739182394623505076034E-33)

249reltol = sqrt(epsilon(1._TKG))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, atad(1:size(data)), reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+86

259data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

260data

261+1.80955148, +1.73321033, +1.65629005, +1.78559256, +1.43515182, +1.90680969, +1.19884026, +1.71933699, +1.19265306, +1.11557770, +1.13695502, +1.90193236, +1.19969320, +1.80917621, +1.92245793, +1.80929029, +1.08235908, +1.95407462, +1.14332879, +1.49685574, +1.10015249, +1.20900452, +1.10061193, +1.28596354, +1.24250364, +1.60603654, +1.74792516, +1.69669139, +1.51749873, +1.80104148, +1.21992826, +1.27221966, +1.28440130, +1.95308805, +1.88431978, +1.74188638, +1.53507912, +1.44202185, +1.90383661, +1.68739581, +1.66309214, +1.16010261, +1.21354461, +1.62809062, +1.97798038, +1.26621962, +1.97083569, +1.42378473, +1.57124591, +1.50364995, +1.24696040, +1.59731102, +1.66606355, +1.14411473, +1.74654305, +1.27831721, +1.58525252, +1.28498459, +1.36242890, +1.75491667, +1.10527122, +1.06428266, +1.98582900, +1.31780291, +1.48258805, +1.83235002, +1.08744836, +1.40018654, +1.96681380, +1.00902128, +1.08446598, +1.48137116, +1.84312785, +1.72394919, +1.99066651, +1.70369744, +1.95444107, +1.07291770, +1.53687835, +1.94400072, +1.95548439, +1.53015494, +1.17220533, +1.40927672, +1.20003748, +1.62471509

262

263atad = getFFTI(getFFTF(data))

264atad

265+1.80955148, +1.73321033, +1.65628982, +1.78559256, +1.43515146, +1.90680957, +1.19883978, +1.71933687, +1.19265318, +1.11557794, +1.13695526, +1.90193260, +1.19969296, +1.80917621, +1.92245793, +1.80929017, +1.08235908, +1.95407474, +1.14332855, +1.49685574, +1.10015237, +1.20900464, +1.10061169, +1.28596354, +1.24250352, +1.60603678, +1.74792480, +1.69669175, +1.51749825, +1.80104148, +1.21992791, +1.27221978, +1.28440142, +1.95308805, +1.88431978, +1.74188614, +1.53507900, +1.44202161, +1.90383661, +1.68739533, +1.66309226, +1.16010261, +1.21354485, +1.62809086, +1.97798014, +1.26621962, +1.97083557, +1.42378426, +1.57124615, +1.50365019, +1.24696016, +1.59731090, +1.66606355, +1.14411473, +1.74654293, +1.27831697, +1.58525240, +1.28498459, +1.36242855, +1.75491667, +1.10527086, +1.06428242, +1.98582876, +1.31780243, +1.48258805, +1.83235002, +1.08744836, +1.40018654, +1.96681368, +1.00902128, +1.08446634, +1.48137105, +1.84312797, +1.72394919, +1.99066639, +1.70369780, +1.95444083, +1.07291770, +1.53687859, +1.94400072, +1.95548463, +1.53015506, +1.17220509, +1.40927672, +1.20003760, +1.62471509, +0.298023224E-6, +0.238418579E-6, +0.238418579E-6, +0.119209290E-6, +0.119209290E-6, +0.178813934E-6, +0.00000000, +0.238418579E-6, -0.238418579E-6, -0.119209290E-6, +0.596046448E-7, +0.119209290E-6, +0.596046448E-7, +0.417232513E-6, -0.119209290E-6, +0.476837158E-6, -0.238418579E-6, +0.417232513E-6, +0.119209290E-6, +0.119209290E-6, +0.178813934E-6, +0.536441803E-6, -0.357627869E-6, +0.178813934E-6, -0.119209290E-6, +0.178813934E-6, +0.178813934E-6, +0.298023224E-6, -0.596046448E-7, +0.357627869E-6, -0.596046448E-7, +0.178813934E-6, -0.596046448E-7, +0.476837158E-6, +0.476837158E-6, +0.238418579E-6, +0.238418579E-6, +0.417232513E-6, -0.596046448E-7, +0.298023224E-6, -0.238418579E-6, +0.00000000

266reltol = sqrt(epsilon(1._TKG))

267reltol

268+0.345266977E-3

269isClose(data, atad(1:size(data)), reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+47

276data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

277data

278+1.1313094760040514, +1.7906106733190972, +1.3361572386697169, +1.9381784306551166, +1.9223966897472051, +1.8664072524312036, +1.3715823138441610, +1.4473536136940726, +1.2418322071271835, +1.8128749792251806, +1.8640368792607991, +1.0918099158741941, +1.0641452771027586, +1.7975855060985007, +1.0161000289791815, +1.2189967173294693, +1.1284162727251832, +1.3918710913455661, +1.3775908806541888, +1.9924495919943475, +1.4811655698610213, +1.3741773301420905, +1.8797043460070098, +1.6448405230708527, +1.9849176689134946, +1.0049704223704761, +1.3200325323961843, +1.8981853187729536, +1.8846182561918483, +1.4448830130792842, +1.6605281817505577, +1.0319539290993407, +1.0526720426084102, +1.3958073978021415, +1.2931008922491118, +1.9046270361766808, +1.5528804107265084, +1.0909253032390496, +1.8061921059888943, +1.4312301597265982, +1.0937881033972530, +1.8509016209275619, +1.6891689632145854, +1.9938846400640970, +1.8089958118272156, +1.6171497067392751, +1.1600022227945610

279

280atad = getFFTI(getFFTF(data))

281atad

282+1.1313094760040516, +1.7906106733190974, +1.3361572386697167, +1.9381784306551175, +1.9223966897472047, +1.8664072524312041, +1.3715823138441605, +1.4473536136940726, +1.2418322071271830, +1.8128749792251806, +1.8640368792607984, +1.0918099158741947, +1.0641452771027584, +1.7975855060985009, +1.0161000289791811, +1.2189967173294696, +1.1284162727251827, +1.3918710913455659, +1.3775908806541883, +1.9924495919943472, +1.4811655698610209, +1.3741773301420903, +1.8797043460070093, +1.6448405230708518, +1.9849176689134937, +1.0049704223704756, +1.3200325323961839, +1.8981853187729527, +1.8846182561918474, +1.4448830130792842, +1.6605281817505571, +1.0319539290993403, +1.0526720426084100, +1.3958073978021410, +1.2931008922491112, +1.9046270361766808, +1.5528804107265080, +1.0909253032390498, +1.8061921059888939, +1.4312301597265980, +1.0937881033972525, +1.8509016209275624, +1.6891689632145854, +1.9938846400640973, +1.8089958118272151, +1.6171497067392757, +1.1600022227945610, +0.0000000000000000, -0.44408920985006262E-15, -0.11102230246251565E-15, +0.11102230246251565E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.0000000000000000, +0.22204460492503131E-15, +0.0000000000000000, +0.11102230246251565E-15, +0.11102230246251565E-15, +0.44408920985006262E-15, +0.99920072216264089E-15, +0.88817841970012523E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, +0.66613381477509392E-15

283reltol = sqrt(epsilon(1._TKG))

284reltol

285+0.14901161193847656E-7

286isClose(data, atad(1:size(data)), reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+43

293data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

294data

295+1.83748734091032868143123792762434518, +1.53414722605585161942600763739954899, +1.08963757005791188520254658441872379, +1.21853497889865894387445189869186829, +1.18375372867304222604267844999182249, +1.68208728996989919775726714512834720, +1.40506315165317630013818991069251933, +1.88263651771057410795831192602304140, +1.61041847222332513891871838814925636, +1.05910273180511753445394839088090711, +1.51826389245422582468202698570502770, +1.53141091892121079562029826659999102, +1.39310341180493115259514600507469873, +1.66669032626867210669769926149039260, +1.33300395774211208160204179251127231, +1.10173509663249353223148542028605668, +1.66667268613538809400067886123114599, +1.50114131787344415131211212239667491, +1.10282450030432744241755540103318163, +1.19874102183820372193546664113354799, +1.60408904311587769594229623831478417, +1.99695624949487675840727230297206019, +1.74462021196051643413682064899660754, +1.86245030651248792759213738360610543, +1.78648282575424882972278963135340078, +1.48345013263126531830484390648476431, +1.75091570303792064240536918566894824, +1.54475633040578100765432620921228966, +1.75903734100376078524537343118670511, +1.57025678116776599877820896241380006, +1.69346258727342741656353303903596300, +1.65491340863486584810772945027681807, +1.54075920174109724190887001736437089, +1.93095330360587166115348897754501102, +1.70264339778065798100397216455344755, +1.47063944342301673574774978033286396, +1.51008159894989714907981266793993191, +1.36862470748981874669109171755513754, +1.18929623036091580636308104746044328, +1.47684314595363894743929835014569451, +1.14996777007738018136861570571275221, +1.77257333239110662448941261807173036, +1.35413848836321697862897271255873936

296

297atad = getFFTI(getFFTF(data))

298atad

299+1.83748734091032868143123792762434518, +1.53414722605585161942600763739954899, +1.08963757005791188520254658441872398, +1.21853497889865894387445189869186868, +1.18375372867304222604267844999182230, +1.68208728996989919775726714512834739, +1.40506315165317630013818991069251933, +1.88263651771057410795831192602304178, +1.61041847222332513891871838814925636, +1.05910273180511753445394839088090711, +1.51826389245422582468202698570502809, +1.53141091892121079562029826659999121, +1.39310341180493115259514600507469893, +1.66669032626867210669769926149039241, +1.33300395774211208160204179251127231, +1.10173509663249353223148542028605687, +1.66667268613538809400067886123114579, +1.50114131787344415131211212239667491, +1.10282450030432744241755540103318163, +1.19874102183820372193546664113354799, +1.60408904311587769594229623831478378, +1.99695624949487675840727230297206019, +1.74462021196051643413682064899660716, +1.86245030651248792759213738360610581, +1.78648282575424882972278963135340078, +1.48345013263126531830484390648476412, +1.75091570303792064240536918566894805, +1.54475633040578100765432620921228966, +1.75903734100376078524537343118670492, +1.57025678116776599877820896241380026, +1.69346258727342741656353303903596300, +1.65491340863486584810772945027681846, +1.54075920174109724190887001736437070, +1.93095330360587166115348897754501102, +1.70264339778065798100397216455344775, +1.47063944342301673574774978033286377, +1.51008159894989714907981266793993133, +1.36862470748981874669109171755513773, +1.18929623036091580636308104746044328, +1.47684314595363894743929835014569490, +1.14996777007738018136861570571275221, +1.77257333239110662448941261807173036, +1.35413848836321697862897271255873975, -0.192592994438723585305597794258492732E-33, -0.577778983316170755916793382775478196E-33, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.192592994438723585305597794258492732E-33, +0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.288889491658085377958396691387739098E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.288889491658085377958396691387739098E-33, +0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, -0.385185988877447170611195588516985464E-33, +0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34

300reltol = sqrt(epsilon(1._TKG))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, atad(1:size(data)), reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+34

310data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

311data

312(+1.89723790, +0.270666063), (+1.48946583, +0.491537750), (+1.91717148, +0.846611202), (+1.99410629, +0.150168478), (+1.13781309, +0.603967786), (+1.51301873, +0.108777225), (+1.87343991, +0.273444891), (+1.84697962, +0.718203127), (+1.11662555, +0.737828910), (+1.22741246, +0.164757609), (+1.12434065, +0.960291922), (+1.55991483, +0.518879652), (+1.90134883, +0.771776438E-1), (+1.55534220, +0.477321625), (+1.91642714, +0.607575834), (+1.24102092, +0.344703794E-1), (+1.31257665, +0.104611278), (+1.08600664, +0.994321227), (+1.52881742, +0.946441472), (+1.81293142, +0.927721262E-1), (+1.38908815, +0.117583215), (+1.13793850, +0.268316984), (+1.40474916, +0.949572027), (+1.15862465, +0.784246147), (+1.03438926, +0.359982967), (+1.15344357, +0.698421121), (+1.77194858, +0.926371217E-1), (+1.12232614, +0.523945272), (+1.66411138, +0.699735701), (+1.15013862, +0.856871545), (+1.05279577, +0.269961774), (+1.28775918, +0.630289674), (+1.43518925, +0.970251679), (+1.54842663, +0.686956048)

313

314atad = getFFTI(getFFTF(data))

315atad

316(+1.89723778, +0.270665914), (+1.48946571, +0.491537780), (+1.91717136, +0.846611023), (+1.99410582, +0.150168344), (+1.13781309, +0.603967667), (+1.51301861, +0.108777188), (+1.87344003, +0.273444653), (+1.84697950, +0.718203008), (+1.11662555, +0.737828851), (+1.22741234, +0.164757639), (+1.12434065, +0.960291743), (+1.55991459, +0.518879771), (+1.90134883, +0.771777630E-1), (+1.55534196, +0.477321744), (+1.91642714, +0.607576013), (+1.24102104, +0.344706811E-1), (+1.31257665, +0.104611203), (+1.08600664, +0.994321108), (+1.52881765, +0.946441233), (+1.81293118, +0.927718580E-1), (+1.38908815, +0.117583208), (+1.13793826, +0.268316984), (+1.40474916, +0.949572086), (+1.15862465, +0.784245849), (+1.03438914, +0.359982967), (+1.15344334, +0.698421121), (+1.77194858, +0.926370621E-1), (+1.12232590, +0.523945034), (+1.66411114, +0.699735761), (+1.15013826, +0.856871486), (+1.05279565, +0.269961774), (+1.28775883, +0.630289555), (+1.43518925, +0.970251560), (+1.54842663, +0.686955929), (+0.357627869E-6, +0.00000000), (+0.298023224E-6, +0.104308128E-6), (-0.596046448E-7, +0.298023224E-7), (+0.596046448E-7, +0.223517418E-7), (-0.596046448E-7, +0.596046448E-7), (+0.119209290E-6, +0.119209290E-6), (+0.596046448E-7, -0.894069672E-7), (+0.119209290E-6, +0.298023224E-7), (+0.238418579E-6, +0.298023224E-7), (+0.298023224E-6, +0.894069672E-7), (+0.596046448E-7, -0.178813934E-6), (+0.119209290E-6, +0.149011612E-7), (+0.119209290E-6, -0.208616257E-6), (-0.119209290E-6, -0.122934580E-6), (+0.119209290E-6, +0.111758709E-7), (+0.00000000, +0.298023224E-7), (+0.596046448E-7, +0.178813934E-6), (+0.119209290E-6, +0.264495611E-6), (+0.596046448E-7, -0.372529030E-7), (+0.596046448E-7, +0.447034836E-7), (+0.596046448E-7, -0.596046448E-7), (+0.238418579E-6, +0.149011612E-6), (+0.119209290E-6, +0.447034836E-7), (+0.178813934E-6, +0.894069672E-7), (+0.596046448E-7, +0.119209290E-6), (+0.178813934E-6, +0.298023224E-6), (+0.298023224E-6, -0.208616257E-6), (+0.238418579E-6, -0.298023224E-7), (+0.119209290E-6, -0.104308128E-6), (-0.596046448E-7, +0.894069672E-7)

317reltol = sqrt(epsilon(1._TKG))

318reltol

319+0.345266977E-3

320isClose(data, atad(1:size(data)), reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+83

327data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

328data

329(+1.5805070955714879, +0.60637992728319712E-1), (+1.0047954164669981, +0.40697507055276494), (+1.7360174975061087, +0.31641605625731772), (+1.8148164317920541, +0.16414197411747733), (+1.1692523185823536, +0.49302310416093076), (+1.1887559147540157, +0.68184501919187168), (+1.4344158614219595, +0.38028256344534317), (+1.2101003519239317, +0.49331187448736991E-1), (+1.9655693505259197, +0.49062292273485997), (+1.0579396231391791, +0.50875856863383950), (+1.4179522288013007, +0.86679992776696357), (+1.8080843289840935, +0.22040436222165050), (+1.6440653652252113, +0.97899737752863358), (+1.4365602057402982, +0.89707821053230452), (+1.7200872922899708, +0.70229087912206623), (+1.9270226459355051, +0.45432894738676077), (+1.6855881158682118, +0.36755877186669228), (+1.3630388194888294, +0.62169164696149581), (+1.0639529911366972, +0.68429136270811819E-1), (+1.4436592540770290, +0.32551193869147821), (+1.2849027612985797, +0.19395509138412081), (+1.5047923533364678, +0.70159502624659864), (+1.2454643645931620, +0.28796828596110768E-1), (+1.6032046665644439, +0.19012920909276243), (+1.7830962468529394, +0.21044012738581996), (+1.7920614275238531, +0.21190729867005575), (+1.3609458891621384, +0.76600808946126908), (+1.6239557458183209, +0.42828265111994912), (+1.3592422048079880, +0.13328441578179373), (+1.5893156078792408, +0.77907066822240034), (+1.6697780736310297, +0.27357343774225817), (+1.6620980206286533, +0.46583200628956212), (+1.3361190501231957, +0.54884982539637028E-1), (+1.1097703302590909, +0.27767504192276871), (+1.7782350873181469, +0.93471341502850536), (+1.9603877708657282, +0.64992362775712820), (+1.9569804214950344, +0.13991043708151996), (+1.9536761297917746, +0.78407066502534628), (+1.4087949309058199, +0.76808913592688099), (+1.0020295020934022, +0.58267689927968558), (+1.0157948129006709, +0.32557033328896179), (+1.5734563097954015, +0.99835659149650757E-1), (+1.2470280532269233, +0.28059673023643494), (+1.2013616526519781, +0.48219886435723358), (+1.5616253758098748, +0.44004209392751237), (+1.3484656034554443, +0.69175388395522575), (+1.1715245736866784, +0.45311904028078331), (+1.0276198545244668, +0.88413413097875093E-1), (+1.3615271357395906, +0.94158031424385125), (+1.5379579166952952, +0.15379916846851505), (+1.7998488818138760, +0.37466366633851766), (+1.9974947103377361, +0.38112721821626927), (+1.3924672314258726, +0.49144352183320184), (+1.0809619878364378, +0.71208144057589717), (+1.5731038338320600, +0.72628527862284997), (+1.6479553207686986, +0.92828319361877620), (+1.7218764763553347, +0.60646472577589439), (+1.8192034666738484, +0.67046243573687292), (+1.3109992580170049, +0.47882563548410650), (+1.5956064957514524, +0.20528562574467280), (+1.3650259592866421, +0.33300456942055223), (+1.5205187436867851, +0.34305962874115536), (+1.2821888190627699, +0.55256609487119401), (+1.7431989305425906, +0.33025770966914603), (+1.7365184453654057, +0.65988983483250541), (+1.2159158691016008, +0.92768835003127348), (+1.3771020546762172, +0.68669924662612636), (+1.1080494063418787, +0.77424315688161605), (+1.2138371224505449, +0.43809781113474455), (+1.7752153195884506, +0.96440107294729782), (+1.0545154585098491, +0.75392741246600714), (+1.5359268787851614, +0.84335893506564052), (+1.5291178318596874, +0.52727721256725424), (+1.1931766092380434, +0.37635714500375017), (+1.5043259071479371, +0.53212566896806568), (+1.5452407514268771, +0.98751794384257630E-1), (+1.4305009191840101, +0.31497927722181107), (+1.5744123342436325, +0.31514723292293056), (+1.8673805391342067, +0.16305767435126917), (+1.1019568235306330, +0.50688438679762460), (+1.1178826362481453, +0.70532289313258367), (+1.1048055926437859, +0.21340765837882913E-1), (+1.6829602984012122, +0.55482169109817614)

330

331atad = getFFTI(getFFTF(data))

332atad

333(+1.5805070955714879, +0.60637992728319712E-1), (+1.0047954164669983, +0.40697507055276527), (+1.7360174975061082, +0.31641605625731783), (+1.8148164317920543, +0.16414197411747772), (+1.1692523185823533, +0.49302310416093065), (+1.1887559147540152, +0.68184501919187224), (+1.4344158614219591, +0.38028256344534328), (+1.2101003519239319, +0.49331187448737379E-1), (+1.9655693505259197, +0.49062292273486036), (+1.0579396231391793, +0.50875856863383984), (+1.4179522288013007, +0.86679992776696391), (+1.8080843289840938, +0.22040436222165125), (+1.6440653652252113, +0.97899737752863369), (+1.4365602057402980, +0.89707821053230508), (+1.7200872922899706, +0.70229087912206656), (+1.9270226459355049, +0.45432894738676133), (+1.6855881158682116, +0.36755877186669211), (+1.3630388194888297, +0.62169164696149604), (+1.0639529911366967, +0.68429136270811763E-1), (+1.4436592540770290, +0.32551193869147821), (+1.2849027612985797, +0.19395509138412070), (+1.5047923533364678, +0.70159502624659864), (+1.2454643645931616, +0.28796828596110990E-1), (+1.6032046665644439, +0.19012920909276249), (+1.7830962468529394, +0.21044012738582027), (+1.7920614275238531, +0.21190729867005600), (+1.3609458891621380, +0.76600808946126886), (+1.6239557458183207, +0.42828265111994940), (+1.3592422048079880, +0.13328441578179395), (+1.5893156078792405, +0.77907066822240023), (+1.6697780736310290, +0.27357343774225829), (+1.6620980206286529, +0.46583200628956178), (+1.3361190501231954, +0.54884982539636820E-1), (+1.1097703302590909, +0.27767504192276860), (+1.7782350873181465, +0.93471341502850502), (+1.9603877708657285, +0.64992362775712820), (+1.9569804214950344, +0.13991043708151965), (+1.9536761297917746, +0.78407066502534595), (+1.4087949309058203, +0.76808913592688088), (+1.0020295020934027, +0.58267689927968547), (+1.0157948129006706, +0.32557033328896168), (+1.5734563097954017, +0.99835659149650646E-1), (+1.2470280532269231, +0.28059673023643472), (+1.2013616526519781, +0.48219886435723358), (+1.5616253758098748, +0.44004209392751226), (+1.3484656034554439, +0.69175388395522530), (+1.1715245736866780, +0.45311904028078309), (+1.0276198545244668, +0.88413413097874927E-1), (+1.3615271357395908, +0.94158031424385114), (+1.5379579166952952, +0.15379916846851494), (+1.7998488818138756, +0.37466366633851744), (+1.9974947103377356, +0.38112721821626933), (+1.3924672314258726, +0.49144352183320172), (+1.0809619878364378, +0.71208144057589684), (+1.5731038338320602, +0.72628527862284953), (+1.6479553207686988, +0.92828319361877587), (+1.7218764763553347, +0.60646472577589416), (+1.8192034666738479, +0.67046243573687259), (+1.3109992580170045, +0.47882563548410617), (+1.5956064957514526, +0.20528562574467257), (+1.3650259592866418, +0.33300456942055195), (+1.5205187436867849, +0.34305962874115481), (+1.2821888190627699, +0.55256609487119346), (+1.7431989305425899, +0.33025770966914569), (+1.7365184453654057, +0.65988983483250541), (+1.2159158691016003, +0.92768835003127337), (+1.3771020546762167, +0.68669924662612647), (+1.1080494063418784, +0.77424315688161593), (+1.2138371224505449, +0.43809781113474477), (+1.7752153195884501, +0.96440107294729749), (+1.0545154585098491, +0.75392741246600692), (+1.5359268787851614, +0.84335893506564008), (+1.5291178318596872, +0.52727721256725446), (+1.1931766092380431, +0.37635714500374984), (+1.5043259071479369, +0.53212566896806568), (+1.5452407514268773, +0.98751794384257435E-1), (+1.4305009191840101, +0.31497927722181107), (+1.5744123342436322, +0.31514723292293023), (+1.8673805391342067, +0.16305767435126906), (+1.1019568235306327, +0.50688438679762404), (+1.1178826362481455, +0.70532289313258367), (+1.1048055926437859, +0.21340765837882469E-1), (+1.6829602984012122, +0.55482169109817603), (+0.11102230246251565E-15, -0.36082248300317588E-15), (+0.66613381477509392E-15, +0.12490009027033011E-15), (+0.11102230246251565E-15, -0.16653345369377348E-15), (+0.33306690738754696E-15, -0.55511151231257827E-16), (+0.33306690738754696E-15, -0.27755575615628914E-15), (+0.11102230246251565E-15, -0.13877787807814457E-15), (-0.11102230246251565E-15, -0.41633363423443370E-15), (+0.0000000000000000, +0.0000000000000000), (+0.22204460492503131E-15, -0.38857805861880479E-15), (+0.55511151231257827E-15, -0.15265566588595902E-15), (+0.44408920985006262E-15, -0.11102230246251565E-15), (+0.22204460492503131E-15, -0.83266726846886741E-16), (+0.11102230246251565E-15, +0.27755575615628914E-16), (+0.11102230246251565E-15, +0.31571967262777889E-15), (-0.22204460492503131E-15, +0.0000000000000000), (-0.55511151231257827E-15, +0.27755575615628914E-15), (-0.11102230246251565E-15, +0.11102230246251565E-15), (+0.0000000000000000, +0.47184478546569153E-15), (-0.22204460492503131E-15, +0.38857805861880479E-15), (-0.11102230246251565E-15, +0.44408920985006262E-15), (-0.44408920985006262E-15, +0.11102230246251565E-15), (+0.0000000000000000, -0.83266726846886741E-16), (+0.22204460492503131E-15, +0.0000000000000000), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.11102230246251565E-15, +0.11102230246251565E-15), (+0.22204460492503131E-15, +0.22204460492503131E-15), (+0.11102230246251565E-15, +0.44408920985006262E-15), (-0.11102230246251565E-15, +0.49960036108132044E-15), (-0.11102230246251565E-15, +0.22204460492503131E-15), (+0.44408920985006262E-15, +0.22204460492503131E-15), (+0.22204460492503131E-15, +0.23592239273284576E-15), (+0.0000000000000000, +0.44408920985006262E-15), (+0.22204460492503131E-15, +0.38857805861880479E-15), (+0.44408920985006262E-15, +0.24980018054066022E-15), (+0.22204460492503131E-15, +0.49960036108132044E-15), (-0.22204460492503131E-15, +0.49960036108132044E-15), (+0.0000000000000000, +0.66613381477509392E-15), (+0.33306690738754696E-15, +0.22204460492503131E-15), (+0.33306690738754696E-15, +0.33306690738754696E-15), (+0.11102230246251565E-15, +0.30531133177191805E-15), (+0.22204460492503131E-15, +0.24980018054066022E-15), (+0.44408920985006262E-15, +0.61062266354383610E-15), (+0.44408920985006262E-15, +0.91593399531575415E-15), (-0.22204460492503131E-15, +0.83266726846886741E-15), (+0.44408920985006262E-15, +0.80491169285323849E-15)

334reltol = sqrt(epsilon(1._TKG))

335reltol

336+0.14901161193847656E-7

337isClose(data, atad(1:size(data)), reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+56

344data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

345data

346(+1.50680390052997240782876649305075137, +0.710027728025677881299719381033798979), (+1.24576218170806783744895466345960487, +0.306833217479620396146843542963992413), (+1.15159517895920106682971740291252220, +0.155424117505933640405400622104807623), (+1.63607932285359374648895972959691715, +0.993366776624035600973315005218729732), (+1.36404923292451667140996928552085511, +0.406084981940222507282063289044579093), (+1.37197824308227069354250383713350767, +0.350869323251566510458679981379174773), (+1.99273709466945309399393016658384664, +0.373735188501967220427357651119997543), (+1.03701982323353651301620112258413906, +0.479295951639976988033261025844994199), (+1.85994733666997870422124727869736545, +0.470733392208986673075023055156279411), (+1.67589189493045133017397588688773549, +0.737309195282463581959874886257509349), (+1.24140649560543225378389201140441573, +0.613094103302283048710280349356511081E-1), (+1.76577142977791610465244410608096140, +0.530264246055094120814898274029285736E-1), (+1.26786380024113022616721973073786543, +0.779057552145853312170179813994392574), (+1.52857752255744375143728857018069188, +0.297666652766900567999290336251352515), (+1.72531514562289386578294425246946772, +0.837442717419698412449742565486339314), (+1.16010096816911114560575484398806048, +0.992281597755940810944553422908820057), (+1.46154864535646877577294557551663874, +0.682734180089505821906089167355863862), (+1.57745688463483984248667488561840527, +0.895622819315021457203501084766264114), (+1.07065950586374045835520767998438127, +0.509822596445514871737825144469695542), (+1.70863190519423039511187130674118744, +0.401935579296715100372548234575478684), (+1.43411429456578173823726061718102219, +0.259199546681766370615729063861095064), (+1.20366907284012305594604091411326737, +0.327187727924396203882813574245729642), (+1.19257719513131695278808752418485572, +0.294320643005905624825307732377048057E-1), (+1.64946463729286477482653756970049939, +0.122377475595321357429786141649453325), (+1.66862479444240942001485280313973992, +0.232638688863999774662574560992992216), (+1.49340877299835497000234850600513447, +0.712403701218466337523704310281617262), (+1.59244343827910721626400935211939648, +0.682526458775797415095967649663552812), (+1.49671706277691894325267617828657190, +0.456072713834161555870812814170087597), (+1.78332915963317252827299349577769525, +0.426576009009022537010833871995716881), (+1.20057445075836158340442017955000023, +0.223424457198707426795459153713904275E-1), (+1.89473126343230516817386640425302843, +0.121749327779384629007541907206846581), (+1.08040306347622273077176877529422871, +0.241276981831219901667972147385215481), (+1.32267582779852353065186511131167245, +0.824219167752069983500040151771286733), (+1.88011989244749077835092251882202973, +0.780425034127368496102607342887104941), (+1.41651514140774193361544594150864001, +0.863360477512026602824492578377131607E-1), (+1.33485061186351860820238216876484566, +0.156857879806776219556691588025717350), (+1.41132959614250641599373594495024166, +0.205812650267642900881870515988200672), (+1.72926454330478698260108950023754204, +0.749452802090595421890197032184619977), (+1.46462259343767988127878707134280446, +0.846890712475838046254202686840885581), (+1.12583325992309336461736544599153658, +0.540497672697224749654405742431899725), (+1.31756883391313947916657776715104315, +0.514670864282226457255851707161825779), (+1.83084563163232890314613505759730548, +0.873994318371666777315885252445000179), (+1.26289488993828159926879419166947999, +0.143711823846258512893220568972078258), (+1.72299252557408265853416226282714647, +0.972475549063720747765240417971702947), (+1.17996442068070628967335351684098252, +0.763984932647013796995616077784979475), (+1.64753580203079608950520028012252722, +0.601147686080633006608499517568684720E-1), (+1.43285540059734938346864216841183692, +0.811266558463639549220166449179119805), (+1.49272783783924154166245773525256021, +0.881792460385859100902158538238124697), (+1.66809660917273845664707407149384055, +0.953159541121133548679694293228214548E-1), (+1.35850770631514376238968308074171059, +0.841164269417444215053806395162960811E-1), (+1.89539680275625478668845453660930655, +0.146971681757781176851076308825712424), (+1.79918526070923150382815764560333827, +0.445174755794825477430247318557747169E-1), (+1.76186874152639555812432216410267421, +0.572823051529122067799960068697292119E-1), (+1.04598256452420841365471524894678432, +0.837124452986669138594858932784738429), (+1.59746287834569644899223699382478396, +0.988264572836466024040169894651705898E-2), (+1.43118597927717202780639902110248208, +0.155829958311827644527930963820209285)

347

348atad = getFFTI(getFFTF(data))

349atad

350(+1.50680390052997240782876649305075156, +0.710027728025677881299719381033798883), (+1.24576218170806783744895466345960449, +0.306833217479620396146843542963992605), (+1.15159517895920106682971740291252201, +0.155424117505933640405400622104807671), (+1.63607932285359374648895972959691657, +0.993366776624035600973315005218729636), (+1.36404923292451667140996928552085531, +0.406084981940222507282063289044578900), (+1.37197824308227069354250383713350747, +0.350869323251566510458679981379174677), (+1.99273709466945309399393016658384664, +0.373735188501967220427357651119997206), (+1.03701982323353651301620112258413906, +0.479295951639976988033261025844994055), (+1.85994733666997870422124727869736565, +0.470733392208986673075023055156279315), (+1.67589189493045133017397588688773530, +0.737309195282463581959874886257509541), (+1.24140649560543225378389201140441573, +0.613094103302283048710280349356511683E-1), (+1.76577142977791610465244410608096120, +0.530264246055094120814898274029288143E-1), (+1.26786380024113022616721973073786581, +0.779057552145853312170179813994392767), (+1.52857752255744375143728857018069169, +0.297666652766900567999290336251352611), (+1.72531514562289386578294425246946791, +0.837442717419698412449742565486339507), (+1.16010096816911114560575484398806048, +0.992281597755940810944553422908820250), (+1.46154864535646877577294557551663874, +0.682734180089505821906089167355863862), (+1.57745688463483984248667488561840507, +0.895622819315021457203501084766264114), (+1.07065950586374045835520767998438107, +0.509822596445514871737825144469695638), (+1.70863190519423039511187130674118763, +0.401935579296715100372548234575478588), (+1.43411429456578173823726061718102238, +0.259199546681766370615729063861094824), (+1.20366907284012305594604091411326679, +0.327187727924396203882813574245729594), (+1.19257719513131695278808752418485553, +0.294320643005905624825307732377045408E-1), (+1.64946463729286477482653756970049977, +0.122377475595321357429786141649453024), (+1.66862479444240942001485280313974011, +0.232638688863999774662574560992992071), (+1.49340877299835497000234850600513447, +0.712403701218466337523704310281617262), (+1.59244343827910721626400935211939648, +0.682526458775797415095967649663552619), (+1.49671706277691894325267617828657190, +0.456072713834161555870812814170087308), (+1.78332915963317252827299349577769544, +0.426576009009022537010833871995716881), (+1.20057445075836158340442017955000004, +0.223424457198707426795459153713900423E-1), (+1.89473126343230516817386640425302843, +0.121749327779384629007541907206846497), (+1.08040306347622273077176877529422871, +0.241276981831219901667972147385215553), (+1.32267582779852353065186511131167265, +0.824219167752069983500040151771286637), (+1.88011989244749077835092251882202934, +0.780425034127368496102607342887105134), (+1.41651514140774193361544594150863981, +0.863360477512026602824492578377131246E-1), (+1.33485061186351860820238216876484527, +0.156857879806776219556691588025717495), (+1.41132959614250641599373594495024185, +0.205812650267642900881870515988200696), (+1.72926454330478698260108950023754185, +0.749452802090595421890197032184620170), (+1.46462259343767988127878707134280427, +0.846890712475838046254202686840885677), (+1.12583325992309336461736544599153658, +0.540497672697224749654405742431899725), (+1.31756883391313947916657776715104334, +0.514670864282226457255851707161825682), (+1.83084563163232890314613505759730529, +0.873994318371666777315885252444999986), (+1.26289488993828159926879419166947999, +0.143711823846258512893220568972078258), (+1.72299252557408265853416226282714628, +0.972475549063720747765240417971702754), (+1.17996442068070628967335351684098271, +0.763984932647013796995616077784979475), (+1.64753580203079608950520028012252703, +0.601147686080633006608499517568684840E-1), (+1.43285540059734938346864216841183692, +0.811266558463639549220166449179119612), (+1.49272783783924154166245773525256021, +0.881792460385859100902158538238124889), (+1.66809660917273845664707407149384055, +0.953159541121133548679694293228215030E-1), (+1.35850770631514376238968308074171039, +0.841164269417444215053806395162959367E-1), (+1.89539680275625478668845453660930655, +0.146971681757781176851076308825712376), (+1.79918526070923150382815764560333827, +0.445174755794825477430247318557749335E-1), (+1.76186874152639555812432216410267440, +0.572823051529122067799960068697291758E-1), (+1.04598256452420841365471524894678394, +0.837124452986669138594858932784738622), (+1.59746287834569644899223699382478396, +0.988264572836466024040169894651703490E-2), (+1.43118597927717202780639902110248247, +0.155829958311827644527930963820209237), (+0.481482486096808963263994485646231830E-33, +0.240741243048404481631997242823115915E-33), (+0.00000000000000000000000000000000000, -0.240741243048404481631997242823115915E-33), (+0.192592994438723585305597794258492732E-33, +0.288889491658085377958396691387739098E-33), (+0.481482486096808963263994485646231830E-33, +0.120370621524202240815998621411557957E-33), (+0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-34), (-0.577778983316170755916793382775478196E-33, -0.288889491658085377958396691387739098E-33), (-0.962964972193617926527988971292463659E-34, +0.180555932286303361223997932117336936E-33), (+0.962964972193617926527988971292463659E-34, +0.120370621524202240815998621411557957E-33)

351reltol = sqrt(epsilon(1._TKG))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, atad(1:size(data)), reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+50

361data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

362data

363+1.58673096, +1.03619957, +1.39473915, +1.04386330, +1.55687416, +1.34161747, +1.28202057, +1.12080550, +1.30891371, +1.85378909, +1.65328288, +1.25959527, +1.17627037, +1.53352094, +1.36876869, +1.71100342, +1.00463533, +1.94520974, +1.48526454, +1.92277980, +1.89288092, +1.95411062, +1.14095116, +1.17080426, +1.74227834, +1.46843505, +1.07029510, +1.62898827, +1.55087399, +1.36962926, +1.63044238, +1.26047111, +1.20768678, +1.12036860, +1.62890577, +1.71189523, +1.59178960, +1.18806195, +1.58409810, +1.34574437, +1.55772781, +1.21639621, +1.58621359, +1.73943329, +1.88473582, +1.82786560, +1.39719367, +1.00953054, +1.44545555, +1.50752950

364

365atad = getFFTI(getFFTF(data))

366atad

367+1.58673120, +1.03619933, +1.39473915, +1.04386294, +1.55687451, +1.34161747, +1.28202081, +1.12080526, +1.30891371, +1.85378873, +1.65328288, +1.25959516, +1.17627048, +1.53352082, +1.36876881, +1.71100295, +1.00463545, +1.94520962, +1.48526466, +1.92277932, +1.89288116, +1.95411062, +1.14095140, +1.17080402, +1.74227834, +1.46843481, +1.07029510, +1.62898803, +1.55087423, +1.36962938, +1.63044238, +1.26047087, +1.20768690, +1.12036848, +1.62890577, +1.71189487, +1.59178996, +1.18806183, +1.58409810, +1.34574413, +1.55772805, +1.21639597, +1.58621383, +1.73943305, +1.88473606, +1.82786548, +1.39719379, +1.00953043, +1.44545567, +1.50752938, +0.119209290E-6, +0.596046448E-7, +0.417232513E-6, +0.596046448E-7, +0.298023224E-6, +0.596046448E-7, +0.417232513E-6, +0.00000000, +0.238418579E-6, +0.238418579E-6, +0.476837158E-6, +0.178813934E-6, +0.238418579E-6, -0.596046448E-7

368reltol = sqrt(epsilon(1._TKG))

369reltol

370+0.345266977E-3

371isClose(data, atad(1:size(data)), reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+61

378data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

379data

380+1.6652377478140266, +1.5310814007071376, +1.1780350389672920, +1.7252138706188147, +1.1017234091456811, +1.0137666028123093, +1.7210608749150973, +1.3713447300235693, +1.9150233694093610, +1.6943090694028284, +1.3455264163221090, +1.6820800999575196, +1.2026381897280392, +1.2011154831571171, +1.0001597578777708, +1.9810216534934244, +1.1971067931553945, +1.8126222484715582, +1.5704424343612180, +1.0075449982903892, +1.4424900305974619, +1.9254266414357000, +1.6209416906649801, +1.8798719074009724, +1.0359804363266947, +1.7539005075799334, +1.2266486389007225, +1.1723276303953982, +1.3955984125382628, +1.6654226913902010, +1.2233313844703295, +1.5123329263767795, +1.2040936202149868, +1.2750195624206122, +1.3354046624691267, +1.5772816910758722, +1.8753514537845080, +1.4903502906245460, +1.7717215483021229, +1.5871254322097705, +1.0436895815324725, +1.0004364320248476, +1.5861745802522678, +1.3897088119244776, +1.7659522874840106, +1.9825628897939609, +1.8358069173561384, +1.1530121410586367, +1.9180524302532311, +1.5646296698215547, +1.8789566429620939, +1.0277918800599690, +1.6235362255012038, +1.0665776195690491, +1.4357291032628254, +1.0220632296232286, +1.1526844768585960, +1.5255602307531508, +1.9229041438051517, +1.0616486026795036, +1.2798296969007199

381

382atad = getFFTI(getFFTF(data))

383atad

384+1.6652377478140268, +1.5310814007071376, +1.1780350389672920, +1.7252138706188147, +1.1017234091456816, +1.0137666028123091, +1.7210608749150971, +1.3713447300235693, +1.9150233694093612, +1.6943090694028289, +1.3455264163221092, +1.6820800999575194, +1.2026381897280394, +1.2011154831571171, +1.0001597578777710, +1.9810216534934246, +1.1971067931553949, +1.8126222484715582, +1.5704424343612178, +1.0075449982903888, +1.4424900305974617, +1.9254266414356995, +1.6209416906649801, +1.8798719074009722, +1.0359804363266951, +1.7539005075799334, +1.2266486389007225, +1.1723276303953980, +1.3955984125382632, +1.6654226913902008, +1.2233313844703297, +1.5123329263767795, +1.2040936202149870, +1.2750195624206122, +1.3354046624691267, +1.5772816910758716, +1.8753514537845080, +1.4903502906245463, +1.7717215483021229, +1.5871254322097705, +1.0436895815324727, +1.0004364320248476, +1.5861745802522678, +1.3897088119244774, +1.7659522874840108, +1.9825628897939609, +1.8358069173561387, +1.1530121410586369, +1.9180524302532316, +1.5646296698215547, +1.8789566429620936, +1.0277918800599686, +1.6235362255012040, +1.0665776195690491, +1.4357291032628252, +1.0220632296232286, +1.1526844768585960, +1.5255602307531513, +1.9229041438051517, +1.0616486026795033, +1.2798296969007201, +0.22204460492503131E-15, +0.55511151231257827E-15, +0.44408920985006262E-15

385reltol = sqrt(epsilon(1._TKG))

386reltol

387+0.14901161193847656E-7

388isClose(data, atad(1:size(data)), reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+33

395data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

396data

397+1.73720532523139314212088482792439777, +1.87678276695965258396248040866288970, +1.74705122773372314759761468240433947, +1.68691516168524834417005747658224544, +1.30371579163872728107607382574082281, +1.24725241654073861087642823810515707, +1.24258966782894767291083180403767831, +1.54360053247959449499717884103154884, +1.95888223136733985698828424920671593, +1.76755306735253342149938455376943124, +1.68497536518055096371840906273092700, +1.36663433604424625011445738675223243, +1.98885688712373615584918184748044579, +1.84062301044818601457991200654961342, +1.60869690159750691216765605793021913, +1.46224953668151812002295650457519611, +1.21286915151738521945056532658866794, +1.83646724213167981699674100167037359, +1.12809577617038694345021469173837041, +1.16962552428674591352341620709817960, +1.04138800406201933109943022201771103, +1.78404118706933126068225474140937864, +1.35497405076419252172289518561429859, +1.75555951202120786018561540301489863, +1.98241209224878893548188568650606999, +1.13651742808173297221406929864583113, +1.42647234323808560929670572889899449, +1.47575332490992753959412925228952819, +1.04596149387791357010007103116435879, +1.35431410356974216830509126412041407, +1.81968810828756041961466858625289829, +1.74868578751978313140537495072660564, +1.35590642688664936376643021045851054

398

399atad = getFFTI(getFFTF(data))

400atad

401+1.73720532523139314212088482792439777, +1.87678276695965258396248040866288970, +1.74705122773372314759761468240433909, +1.68691516168524834417005747658224544, +1.30371579163872728107607382574082320, +1.24725241654073861087642823810515707, +1.24258966782894767291083180403767870, +1.54360053247959449499717884103154884, +1.95888223136733985698828424920671632, +1.76755306735253342149938455376943124, +1.68497536518055096371840906273092739, +1.36663433604424625011445738675223243, +1.98885688712373615584918184748044656, +1.84062301044818601457991200654961342, +1.60869690159750691216765605793021990, +1.46224953668151812002295650457519611, +1.21286915151738521945056532658866813, +1.83646724213167981699674100167037340, +1.12809577617038694345021469173837060, +1.16962552428674591352341620709817999, +1.04138800406201933109943022201771103, +1.78404118706933126068225474140937903, +1.35497405076419252172289518561429897, +1.75555951202120786018561540301489883, +1.98241209224878893548188568650607018, +1.13651742808173297221406929864583132, +1.42647234323808560929670572889899487, +1.47575332490992753959412925228952819, +1.04596149387791357010007103116435860, +1.35431410356974216830509126412041446, +1.81968810828756041961466858625289848, +1.74868578751978313140537495072660584, +1.35590642688664936376643021045851093, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.962964972193617926527988971292463659E-34, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, -0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.385185988877447170611195588516985464E-33, -0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, -0.577778983316170755916793382775478196E-33, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33, -0.192592994438723585305597794258492732E-33, +0.962964972193617926527988971292463659E-34, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, -0.288889491658085377958396691387739098E-33, -0.192592994438723585305597794258492732E-33, +0.00000000000000000000000000000000000, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, +0.192592994438723585305597794258492732E-33, +0.192592994438723585305597794258492732E-33, -0.288889491658085377958396691387739098E-33, -0.962964972193617926527988971292463659E-34, +0.192592994438723585305597794258492732E-33

402reltol = sqrt(epsilon(1._TKG))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, atad(1:size(data)), reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+9

412data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

413data

414(+1.40352750, +0.523820937), (+1.54144621, +0.388165057), (+1.78133583, +0.390089929), (+1.57315469, +0.481643617), (+1.26507926, +0.952089429), (+1.20072484, +0.360178888), (+1.09346247, +0.520704627), (+1.34101689, +0.793189824), (+1.77533126, +0.239786386)

415

416atad = getFFTI(getFFTF(data))

417atad

418(+1.40352750, +0.523820937), (+1.54144621, +0.388165116), (+1.78133547, +0.390089929), (+1.57315445, +0.481643736), (+1.26507938, +0.952089310), (+1.20072484, +0.360178828), (+1.09346247, +0.520704269), (+1.34101677, +0.793189585), (+1.77533126, +0.239786446), (+0.00000000, -0.149011612E-7), (+0.119209290E-6, +0.00000000), (+0.119209290E-6, -0.596046448E-7), (+0.00000000, +0.119209290E-6), (+0.00000000, +0.298023224E-7), (+0.00000000, +0.268220901E-6), (+0.119209290E-6, +0.178813934E-6)

419reltol = sqrt(epsilon(1._TKG))

420reltol

421+0.345266977E-3

422isClose(data, atad(1:size(data)), reltol = reltol)

423T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+31

429data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

430data

431(+1.8575635661771532, +0.50449313764519677), (+1.4132393368366916, +0.65488457909259723E-1), (+1.0090747133714328, +0.32247296460692076), (+1.0724538745904941, +0.39673777924297160E-1), (+1.9415378744292642, +0.92213288601153076E-1), (+1.8433094510676469, +0.97400973257582202), (+1.9402958207267424, +0.37872591813057466E-1), (+1.8175078186329436, +0.32080488951920016), (+1.0678938717937805, +0.32124674304307788), (+1.6817691877897498, +0.90767719225473342), (+1.3306027137827892, +0.93002476384412269), (+1.9992966093205105, +0.53264104892092323), (+1.0625651228826580, +0.46224611521017300), (+1.9416201849453114, +0.75622714585123907), (+1.5256411092309625, +0.11763396461865172), (+1.6326335502412901, +0.23042285580724897), (+1.6730699177181698, +0.89568675167994327), (+1.7842988402974829, +0.74017204792939439), (+1.7052229282532991, +0.84965324466822367E-1), (+1.1992624383804329, +0.86800297262489834), (+1.0046874219345754, +0.92685067489408779), (+1.9169646548178689, +0.54037755219327799), (+1.6361631064947728, +0.70179333783618159), (+1.9453632065634814, +0.26871528894298158), (+1.3846498164082823, +0.78782364237704627), (+1.4680814719255044, +0.90018472153359252), (+1.6752505225016989, +0.96024284159726248), (+1.2481671706546984, +0.56254888235782985), (+1.8403321524901215, +0.97186801326228889), (+1.1634489326264652, +0.38798239910015953), (+1.0922178249263435, +0.87605905849055088)

432

433atad = getFFTI(getFFTF(data))

434atad

435(+1.8575635661771528, +0.50449313764519688), (+1.4132393368366916, +0.65488457909259945E-1), (+1.0090747133714333, +0.32247296460692076), (+1.0724538745904939, +0.39673777924297493E-1), (+1.9415378744292640, +0.92213288601153354E-1), (+1.8433094510676467, +0.97400973257582191), (+1.9402958207267427, +0.37872591813057799E-1), (+1.8175078186329432, +0.32080488951920011), (+1.0678938717937803, +0.32124674304307815), (+1.6817691877897498, +0.90767719225473320), (+1.3306027137827894, +0.93002476384412280), (+1.9992966093205100, +0.53264104892092323), (+1.0625651228826580, +0.46224611521017323), (+1.9416201849453112, +0.75622714585123885), (+1.5256411092309627, +0.11763396461865205), (+1.6326335502412894, +0.23042285580724889), (+1.6730699177181696, +0.89568675167994338), (+1.7842988402974826, +0.74017204792939417), (+1.7052229282532994, +0.84965324466822562E-1), (+1.1992624383804327, +0.86800297262489834), (+1.0046874219345754, +0.92685067489408812), (+1.9169646548178687, +0.54037755219327788), (+1.6361631064947730, +0.70179333783618159), (+1.9453632065634809, +0.26871528894298163), (+1.3846498164082821, +0.78782364237704661), (+1.4680814719255044, +0.90018472153359219), (+1.6752505225016991, +0.96024284159726259), (+1.2481671706546982, +0.56254888235782974), (+1.8403321524901211, +0.97186801326228889), (+1.1634489326264654, +0.38798239910015964), (+1.0922178249263439, +0.87605905849055088), (+0.66613381477509392E-15, +0.30531133177191805E-15)

436reltol = sqrt(epsilon(1._TKG))

437reltol

438+0.14901161193847656E-7

439isClose(data, atad(1:size(data)), reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+29

446data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

447data

448(+1.17104117152931413073464852509954181, +0.739274356662771375598558301889296898), (+1.21641590628661608226083904137486999, +0.208820071592686301538711789950140943), (+1.26859192563524381465994707058240641, +0.533421277939838941666412757846575337), (+1.52109837132289235492333726539994383, +0.908502092331497765439105329890650125), (+1.47618886645886050820987722691055829, +0.788746665243455035601664617370177602), (+1.60715325635790367271977815037241827, +0.251071374469912920520481861992941011), (+1.67713051465328800304345830766187323, +0.137090233935362395551623541732978077), (+1.08586350728811610109978806695171080, +0.748383898123769492570604375649663795), (+1.81923753135810929660133566529730356, +0.925755398502605900702023839529063184), (+1.89343305373635078579866196605754907, +0.620046651252740963404897409814046459), (+1.10404196046647152739708436337662685, +0.600165847794678760431955745105361602), (+1.05359466796709995106781463597144357, +0.713532168226122913232475676699528761), (+1.06158969414579108512521553707791476, +0.108582646079209734899679373277766383), (+1.26200754658250747298343142375047459, +0.471632496138398394495360030012384240), (+1.03809138013077725076906039626815336, +0.606856854909273132646298080648565210), (+1.19139607575777625811670317177938253, +0.618584284571598486989736281118398493), (+1.95990020360495964973483355780487894, +0.838970226317954198393192998864467910E-1), (+1.15401012281714024582120813682849859, +0.922832750914571647003922545227216446), (+1.18039293284040635118138424364691638, +0.887812174547150660005906692468418258), (+1.14220092667858248609203082853044612, +0.281870591546921465731191669668481350E-1), (+1.09371532434346094823487268878069269, +0.117157350359348876660114409751026156), (+1.81525402925072182088654444448070825, +0.869666160644793253733324051683052675), (+1.23719207748576344969517887158288400, +0.173961520412798841282397107173043975E-1), (+1.71459003702552272590235130966746046, +0.352706843534359267441209943187978490), (+1.11830812502883125403916397265210012, +0.743549884609846008264996221657293177), (+1.79782757159126553565133398233491716, +0.718139452634034389605553784493125579), (+1.86811094992786118585909146105858747, +0.691297386388648605181631123232927118), (+1.98706949443359307136736073942305990, +0.156144560381130804711633990510951356), (+1.82105015380452527089637406804697066, +0.400138701149913410060778706888400489)

449

450atad = getFFTI(getFFTF(data))

451atad

452(+1.17104117152931413073464852509954162, +0.739274356662771375598558301889296898), (+1.21641590628661608226083904137486999, +0.208820071592686301538711789950140991), (+1.26859192563524381465994707058240660, +0.533421277939838941666412757846575337), (+1.52109837132289235492333726539994383, +0.908502092331497765439105329890650317), (+1.47618886645886050820987722691055867, +0.788746665243455035601664617370177698), (+1.60715325635790367271977815037241847, +0.251071374469912920520481861992940915), (+1.67713051465328800304345830766187342, +0.137090233935362395551623541732977956), (+1.08586350728811610109978806695171080, +0.748383898123769492570604375649663603), (+1.81923753135810929660133566529730356, +0.925755398502605900702023839529063184), (+1.89343305373635078579866196605754907, +0.620046651252740963404897409814046363), (+1.10404196046647152739708436337662685, +0.600165847794678760431955745105361698), (+1.05359466796709995106781463597144357, +0.713532168226122913232475676699528569), (+1.06158969414579108512521553707791495, +0.108582646079209734899679373277766358), (+1.26200754658250747298343142375047439, +0.471632496138398394495360030012384240), (+1.03809138013077725076906039626815298, +0.606856854909273132646298080648565307), (+1.19139607575777625811670317177938215, +0.618584284571598486989736281118398493), (+1.95990020360495964973483355780487894, +0.838970226317954198393192998864468392E-1), (+1.15401012281714024582120813682849878, +0.922832750914571647003922545227216350), (+1.18039293284040635118138424364691619, +0.887812174547150660005906692468418355), (+1.14220092667858248609203082853044612, +0.281870591546921465731191669668480387E-1), (+1.09371532434346094823487268878069288, +0.117157350359348876660114409751026060), (+1.81525402925072182088654444448070863, +0.869666160644793253733324051683052579), (+1.23719207748576344969517887158288400, +0.173961520412798841282397107173042229E-1), (+1.71459003702552272590235130966746066, +0.352706843534359267441209943187978393), (+1.11830812502883125403916397265210012, +0.743549884609846008264996221657293177), (+1.79782757159126553565133398233491716, +0.718139452634034389605553784493125387), (+1.86811094992786118585909146105858747, +0.691297386388648605181631123232927407), (+1.98706949443359307136736073942305990, +0.156144560381130804711633990510951308), (+1.82105015380452527089637406804697085, +0.400138701149913410060778706888400393), (+0.192592994438723585305597794258492732E-33, +0.240741243048404481631997242823115915E-34), (-0.962964972193617926527988971292463659E-34, -0.481482486096808963263994485646231830E-34), (-0.962964972193617926527988971292463659E-34, +0.481482486096808963263994485646231830E-34)

453reltol = sqrt(epsilon(1._TKG))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, atad(1:size(data)), reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+6

463data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

464data

465+1.80932140, +1.34669507, +1.27094531, +1.66363049, +1.10457778, +1.02638364

466

467atad = getFFTI(getFFTF(data))

468atad

469+1.80932140, +1.34669507, +1.27094531, +1.66363025, +1.10457778, +1.02638376, -0.596046448E-7, +0.238418579E-6

470reltol = sqrt(epsilon(1._TKG))

471reltol

472+0.345266977E-3

473isClose(data, atad(1:size(data)), reltol = reltol)

474T, T, T, T, T, T

475call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+78

480data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

481data

482+1.1632725079281132, +1.7006760006857988, +1.5324656697983303, +1.0633160727745476, +1.7011579575914852, +1.2251513250018509, +1.6342553691129855, +1.0500533204069382, +1.6336425429023085, +1.5982985088138020, +1.1136389059017375, +1.9021418687227727, +1.2925017082257420, +1.1309766330967475, +1.7687540851079371, +1.7481052006092872, +1.5790798891873026, +1.0794304707889446, +1.6352985685663535, +1.1874021814113380, +1.4975048669139754, +1.2608113340355158, +1.0948338088962051, +1.0048810639941474, +1.8145428438706181, +1.2257106958403643, +1.6171325917466346, +1.3974231461926085, +1.5757417731920902, +1.3203266120489614, +1.4443509344483949, +1.0928241422957217, +1.0332828159710195, +1.2214462848790426, +1.1819197413723708, +1.3737688466793165, +1.8374633129971247, +1.9048949707587108, +1.8275464772473171, +1.6312397558259228, +1.0480896022316843, +1.6414392187253379, +1.4974124387649146, +1.4866949936193707, +1.2061541679377301, +1.9323519496985710, +1.3387444716094996, +1.2663205214649893, +1.8615460394911747, +1.1191856205247253, +1.0666998261453404, +1.9926119590316509, +1.6122059798104373, +1.5280768296670533, +1.0133083583391789, +1.7460711586499622, +1.3671386337605498, +1.8089943376912383, +1.0463094009615068, +1.2187133620715942, +1.4265198605346774, +1.5261948093477331, +1.7258080975140284, +1.7942785765318741, +1.9404418979713456, +1.4308730739620625, +1.2499157016720224, +1.4435189033139126, +1.0856130289462760, +1.7983893354323353, +1.3282254574376342, +1.5797946067828323, +1.3553376312507175, +1.4056970061733001, +1.6906597937816485, +1.9653265046848203, +1.7704506706695842, +1.1174641436702513

483

484atad = getFFTI(getFFTF(data))

485atad

486+1.1632725079281130, +1.7006760006857988, +1.5324656697983303, +1.0633160727745481, +1.7011579575914848, +1.2251513250018506, +1.6342553691129846, +1.0500533204069391, +1.6336425429023080, +1.5982985088138022, +1.1136389059017375, +1.9021418687227731, +1.2925017082257417, +1.1309766330967475, +1.7687540851079366, +1.7481052006092876, +1.5790798891873024, +1.0794304707889446, +1.6352985685663533, +1.1874021814113385, +1.4975048669139750, +1.2608113340355156, +1.0948338088962042, +1.0048810639941474, +1.8145428438706173, +1.2257106958403650, +1.6171325917466342, +1.3974231461926085, +1.5757417731920895, +1.3203266120489614, +1.4443509344483936, +1.0928241422957219, +1.0332828159710192, +1.2214462848790426, +1.1819197413723703, +1.3737688466793161, +1.8374633129971247, +1.9048949707587108, +1.8275464772473164, +1.6312397558259222, +1.0480896022316841, +1.6414392187253384, +1.4974124387649144, +1.4866949936193707, +1.2061541679377306, +1.9323519496985710, +1.3387444716094994, +1.2663205214649889, +1.8615460394911745, +1.1191856205247250, +1.0666998261453400, +1.9926119590316502, +1.6122059798104376, +1.5280768296670528, +1.0133083583391791, +1.7460711586499609, +1.3671386337605496, +1.8089943376912376, +1.0463094009615066, +1.2187133620715938, +1.4265198605346776, +1.5261948093477327, +1.7258080975140282, +1.7942785765318729, +1.9404418979713456, +1.4308730739620625, +1.2499157016720224, +1.4435189033139122, +1.0856130289462762, +1.7983893354323355, +1.3282254574376346, +1.5797946067828319, +1.3553376312507170, +1.4056970061733003, +1.6906597937816485, +1.9653265046848203, +1.7704506706695842, +1.1174641436702513, +0.33306690738754696E-15, -0.33306690738754696E-15, +0.0000000000000000, -0.11102230246251565E-15, +0.55511151231257827E-15, -0.44408920985006262E-15, +0.66613381477509392E-15, +0.0000000000000000, +0.99920072216264089E-15, -0.11102230246251565E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, +0.44408920985006262E-15, +0.22204460492503131E-15, +0.11102230246251565E-14, -0.22204460492503131E-15, -0.22204460492503131E-15, +0.22204460492503131E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, -0.55511151231257827E-15, +0.44408920985006262E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, -0.33306690738754696E-15, +0.11102230246251565E-15, -0.11102230246251565E-15, +0.0000000000000000, -0.33306690738754696E-15, +0.11102230246251565E-15, -0.22204460492503131E-15, +0.55511151231257827E-15, -0.33306690738754696E-15, +0.22204460492503131E-15, +0.0000000000000000, +0.44408920985006262E-15, -0.55511151231257827E-15, +0.55511151231257827E-15, -0.44408920985006262E-15, +0.88817841970012523E-15, -0.11102230246251565E-15, +0.66613381477509392E-15, +0.44408920985006262E-15, +0.33306690738754696E-15, -0.22204460492503131E-15, +0.33306690738754696E-15, -0.11102230246251565E-15, +0.11102230246251565E-14

487reltol = sqrt(epsilon(1._TKG))

488reltol

489+0.14901161193847656E-7

490isClose(data, atad(1:size(data)), reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+19

497data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

498data

499+1.58136776435836594100896345577749789, +1.95282907255966144441234432593546583, +1.91254552463884783294547540833275690, +1.18443207762139014974695256668790243, +1.58309674232220801437024956685363346, +1.36062407978646867844545066553027663, +1.51551346741176065625285414672782371, +1.16197040479325648788090996161182462, +1.58659644940667459980509308745965467, +1.82692116446062787904880542868761301, +1.13351984721251448879437467558716286, +1.15615444274432317098623036428203079, +1.78178004345385123661534339718438647, +1.98982572389562759403730150086762555, +1.29170129465797519518547915137065141, +1.35331247058091200173797439324248327, +1.61519722890802943421089985675803123, +1.47046797735270754889332956852098554, +1.23504252940111622187249112612571028

500

501atad = getFFTI(getFFTF(data))

502atad

503+1.58136776435836594100896345577749770, +1.95282907255966144441234432593546583, +1.91254552463884783294547540833275710, +1.18443207762139014974695256668790282, +1.58309674232220801437024956685363346, +1.36062407978646867844545066553027663, +1.51551346741176065625285414672782371, +1.16197040479325648788090996161182519, +1.58659644940667459980509308745965467, +1.82692116446062787904880542868761301, +1.13351984721251448879437467558716305, +1.15615444274432317098623036428203098, +1.78178004345385123661534339718438686, +1.98982572389562759403730150086762555, +1.29170129465797519518547915137065180, +1.35331247058091200173797439324248327, +1.61519722890802943421089985675803123, +1.47046797735270754889332956852098534, +1.23504252940111622187249112612570990, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, +0.00000000000000000000000000000000000, -0.288889491658085377958396691387739098E-33, -0.288889491658085377958396691387739098E-33, -0.385185988877447170611195588516985464E-33, -0.962964972193617926527988971292463659E-34, -0.577778983316170755916793382775478196E-33, -0.385185988877447170611195588516985464E-33, -0.577778983316170755916793382775478196E-33, +0.962964972193617926527988971292463659E-34, -0.385185988877447170611195588516985464E-33, +0.00000000000000000000000000000000000

504reltol = sqrt(epsilon(1._TKG))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, atad(1:size(data)), reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, atad(1:size(data)), reltol = reltol)))

510

511

Test:: test_pm_fftnr

Final Remarks ⛓

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Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 250 of file pm_fftnr.F90.

The documentation for this interface was generated from the following file:

src/fortran/main/pm_fftnr.F90